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Write the composite function in the form fg(x). [Identify the innerfunction u g(x) and the outer function y = f{u).] Then find the derivativedy/dxy = evT

Question

Please show as much steps as possible as I am doing my best to fully understand how to solve these type of problems. The solutions manual only helps so much but it tends to skip minor details that are of critical value. Thx in advance.

Write the composite function in the form fg(x). [Identify the inner
function u g(x) and the outer function y = f{u).] Then find the derivative
dy/dx
y = evT
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Write the composite function in the form fg(x). [Identify the inner function u g(x) and the outer function y = f{u).] Then find the derivative dy/dx y = evT

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Step 1

Given function is,

 

ア=evi
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ア=evi

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Step 2

It is the composition of two functions, namely

 

и- g(x)-\x
апd у —f (u)-е'
(8(x)()e
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и- g(x)-\x апd у —f (u)-е' (8(x)()e

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Step 3

Now differentiating the given function wit...

dy d
dr dr
d
()
=ev
dr
-(e') = x
dx
1
d
2x
dx
eve
2/x
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dy d dr dr d () =ev dr -(e') = x dx 1 d 2x dx eve 2/x

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Tagged in

Math

Calculus

Derivative

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