5.3 :Higher Order Derivatives, Concavity and the 2 nd Derivative Test
Engineering Mathematics - Total derivatives, chain rule and derivative of implicit functions
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Transcript of Engineering Mathematics - Total derivatives, chain rule and derivative of implicit functions
Total Derivative
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Total Derivative
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Total Derivative
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The Chain Rule
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∂∂∗
∂∂+
∂∂∗
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∂∂∗
∂∂=
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∂∂+
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∂∂=
∂∂
=====
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The Chain Rule
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∗∂∂+∗
∂∂=
∂∂
∗∂∂+∗
∂∂=
∂∂∗
∂∂+
∂∂∗
∂∂=
∂∂
∂∂=∗
∂∂+∗
∂∂=
∂∂∗
∂∂+
∂∂∗
∂∂=
∂∂
∂∂=∗
∂∂+∗
∂∂=
∂∂∗
∂∂+
∂∂∗
∂∂=
∂∂
∂∂+
∂∂=
∂∂
+=+==
(3)& (2) (1), From
)3.........(....................
)2(....................10
)1.........(..........01 Ans.
: that show then s,t variableindependen theare t &y x,&bt ys at,xr s),f(r,u
:Example
Derivative Of Implicit Functions
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Derivative Of Implicit Functions
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:Example
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∗+∗=∂∂
=∂∂
==+
=+∂∂
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