<?xml version="1.0" encoding="us-ascii"?><InstanceReport xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><Version>2.4.0.8</Version><ReportLongName>115 - Disclosure - Derivative Financial Instruments</ReportLongName><DisplayLabelColumn>true</DisplayLabelColumn><ShowElementNames>false</ShowElementNames><RoundingOption /><HasEmbeddedReports>false</HasEmbeddedReports><Columns><Column FlagID="0"><Id>1</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><CurrencyCode /><FootnoteIndexer /><hasSegments>false</hasSegments><hasScenarios>false</hasScenarios><MCU><KeyName /><CurrencySymbol /><contextRef><ContextID>eol_PE71016---1310-Q0006_STD_181_20130630_0</ContextID><EntitySchema>http://www.sec.gov/CIK</EntitySchema><EntityValue>0001103021</EntityValue><PeriodDisplayName /><PeriodType>duration</PeriodType><PeriodStartDate>2013-01-01T00:00:00</PeriodStartDate><PeriodEndDate>2013-06-30T00:00:00</PeriodEndDate><Segments /><Scenarios /></contextRef><UPS /><CurrencyCode /><OriginalCurrencyCode /></MCU><CurrencySymbol /><Labels><Label Key="CalendarSupplement" Id="0" Label="6 Months Ended" /><Label Key="Calendar" Id="1" Label="Jun. 30, 2013" /></Labels></Column></Columns><Rows><Row FlagID="0"><Id>1</Id><IsAbstractGroupTitle>true</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>1</Level><ElementName>us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureAbstract</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText /><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>xbrli:stringItemType</ElementDataType><SimpleDataType>string</SimpleDataType><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Derivative Instruments And Hedging Activities Disclosure [Abstract]</Label></Row><Row FlagID="0"><Id>2</Id><IsAbstractGroupTitle>false</IsAbstractGroupTitle><LabelSeparator>

</LabelSeparator><Level>2</Level><ElementName>us-gaap_DerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock</ElementName><ElementPrefix>us-gaap_</ElementPrefix><IsBaseElement>true</IsBaseElement><BalanceType>na</BalanceType><PeriodType>duration</PeriodType><IsReportTitle>false</IsReportTitle><IsSegmentTitle>false</IsSegmentTitle><IsCalendarTitle>false</IsCalendarTitle><IsEquityPrevioslyReportedAsRow>false</IsEquityPrevioslyReportedAsRow><IsEquityAdjustmentRow>false</IsEquityAdjustmentRow><IsBeginningBalance>false</IsBeginningBalance><IsEndingBalance>false</IsEndingBalance><IsReverseSign>false</IsReverseSign><PreferredLabelRole>terseLabel</PreferredLabelRole><FootnoteIndexer /><Cells><Cell FlagID="0" ContextID="eol_PE71016---1310-Q0006_STD_181_20130630_0" UnitID=""><Id>1</Id><IsNumeric>false</IsNumeric><IsRatio>false</IsRatio><DisplayZeroAsNone>false</DisplayZeroAsNone><NumericAmount>0</NumericAmount><RoundedNumericAmount>0</RoundedNumericAmount><NonNumbericText>&lt;div&gt;
&lt;table style="BORDER-COLLAPSE: collapse" border="0" cellspacing="0" cellpadding="0" width="100%"&gt;
&lt;tr&gt;
&lt;td valign="top" width="4%" align="left"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;8.&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;td valign="top" align="left"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;&lt;b&gt;Derivative Financial
Instruments:&lt;/b&gt;&lt;/font&gt;&lt;/td&gt;
&lt;/tr&gt;
&lt;/table&gt;
&lt;p style="MARGIN-TOP: 6px; MARGIN-BOTTOM: 0px"&gt;&lt;font style="FONT-FAMILY: Times New Roman" size="2"&gt;The Company generally does
not use derivative instruments to hedge exposures to cash-flow
risks or market-risks that may affect the fair values of its
financial instruments. However, certain other financial
instruments, such as warrants and embedded conversion features that
are indexed to the Company&amp;#x2019;s Common Stock, are classified as
liabilities when either: (a)&amp;#xA0;the holder possesses rights to
net-cash settlement or (b)&amp;#xA0;physical or net-share settlement is
not within the control of the Company. In such instances, net-cash
settlement is assumed for financial accounting and reporting, even
when the terms of the underlying contracts do not provide for
net-cash settlement. Such financial instruments are initially
recorded at fair value estimated on the settlement date using the
Black-Scholes valuation model that uses assumptions for expected
volatility, expected dividends, expected term, and the risk-free
interest rate, and then adjusted to fair value at the close of each
reporting period.&lt;/font&gt;&lt;/p&gt;
&lt;/div&gt;</NonNumbericText><FootnoteIndexer /><CurrencyCode /><CurrencySymbol /><IsIndependantCurrency>false</IsIndependantCurrency><ShowCurrencySymbol>false</ShowCurrencySymbol><DisplayDateInUSFormat>false</DisplayDateInUSFormat></Cell></Cells><ElementDataType>nonnum:textBlockItemType</ElementDataType><SimpleDataType>na</SimpleDataType><ElementDefenition>The entire disclosure for derivative instruments and hedging activities including, but not limited to, risk management strategies, non-hedging derivative instruments, assets, liabilities, revenue and expenses, and methodologies and assumptions used in determining the amounts.</ElementDefenition><ElementReferences>Reference 1: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4K

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5708775-113959



Reference 2: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4B

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5624163-113959



Reference 3: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 235

 -SubTopic 10

 -Section S99

 -Paragraph 1

 -Subparagraph (SX 210.4-08.(n))

 -URI http://asc.fasb.org/extlink&amp;oid=26873400&amp;loc=d3e23780-122690



Reference 4: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4J

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5708773-113959



Reference 5: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 25

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6886632&amp;loc=d3e76258-113986



Reference 6: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 3

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=d3e41635-113959



Reference 7: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4H

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5624258-113959



Reference 8: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4A

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5618551-113959



Reference 9: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 30

 -Section 45

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=6441202&amp;loc=d3e80720-113993



Reference 10: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 30

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=7668309&amp;loc=d3e80748-113994



Reference 11: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4E

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5624181-113959



Reference 12: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 30

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=7668309&amp;loc=d3e80784-113994



Reference 13: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 2

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=d3e41620-113959



Reference 14: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4D

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5624177-113959



Reference 15: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 1A

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5579245-113959



Reference 16: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 1B

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5580258-113959



Reference 17: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 1

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5579240-113959



Reference 18: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 5

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=d3e41641-113959



Reference 19: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=d3e41638-113959



Reference 20: http://www.xbrl.org/2003/role/presentationRef

 -Publisher FASB

 -Name Accounting Standards Codification

 -Topic 815

 -SubTopic 10

 -Section 50

 -Paragraph 4C

 -URI http://asc.fasb.org/extlink&amp;oid=7476318&amp;loc=SL5624171-113959



</ElementReferences><IsTotalLabel>false</IsTotalLabel><UnitID>0</UnitID><Label>Derivative Financial Instruments</Label></Row></Rows><Footnotes /><IsEquityReport>false</IsEquityReport><ReportName>Derivative Financial Instruments</ReportName><MonetaryRoundingLevel>UnKnown</MonetaryRoundingLevel><SharesRoundingLevel>UnKnown</SharesRoundingLevel><PerShareRoundingLevel>UnKnown</PerShareRoundingLevel><ExchangeRateRoundingLevel>UnKnown</ExchangeRateRoundingLevel><HasCustomUnits>true</HasCustomUnits><IsEmbedReport>false</IsEmbedReport><IsMultiCurrency>false</IsMultiCurrency><ReportType>Sheet</ReportType><RoleURI>http://www.bdsi.com/taxonomy/role/NotesToFinancialStatementsDerivativeInstrumentsAndHedgingActivitiesDisclosureTextBlock</RoleURI><NumberOfCols>1</NumberOfCols><NumberOfRows>2</NumberOfRows></InstanceReport>
