Example 5:Use the Second Form of the Chain Rule to find the derivative of each function. Verify thateach function is a composite function by identifying the outside function g and the insidefunction h. Identify the Rate-of-Change Rule used in finding the derivative of the outsidefunction. Use proper notation.a. f(x)= (-3x +2x-5)-2f'(x) =f(x) = V -3x +2x -5S'(x)= CoXt 2x2 5CoxtZx131 -2f(x) = (In (x))с.d. f(x) 3/In (x)f(x) = In (-3x2 +2x-5)е.f. f(x) 2ln (x)

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Asked Nov 1, 2019
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I need help with e. and d.

 

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Example 5:
Use the Second Form of the Chain Rule to find the derivative of each function. Verify that
each function is a composite function by identifying the outside function g and the inside
function h. Identify the Rate-of-Change Rule used in finding the derivative of the outside
function. Use proper notation.
a. f(x)= (-3x +2x-5)-2
f'(x) =
f(x) = V -3x +2x -5
S'(x)= CoXt 2x
2 5
CoxtZx
131
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Example 5: Use the Second Form of the Chain Rule to find the derivative of each function. Verify that each function is a composite function by identifying the outside function g and the inside function h. Identify the Rate-of-Change Rule used in finding the derivative of the outside function. Use proper notation. a. f(x)= (-3x +2x-5)-2 f'(x) = f(x) = V -3x +2x -5 S'(x)= CoXt 2x 2 5 CoxtZx 131

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-2
f(x) = (In (x))
с.
d. f(x) 3/In (x)
f(x) = In (-3x2 +2x-5)
е.
f. f(x) 2ln (x)
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-2 f(x) = (In (x)) с. d. f(x) 3/In (x) f(x) = In (-3x2 +2x-5) е. f. f(x) 2ln (x)

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Expert Answer

Step 1

(d)

Consider the given function:

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f(x)3in(x)

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Step 2

Here, let

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y g(u)3/u and uh(x)=nx

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Step 3

So, f(x) is a composition function that can be written as:

f(x)=g(h(x))=(g o h)(x)

Now,...

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dy dy du dx du dx dy d d (3Vu (3Jm)(In x) Inx) ( dx du 3 1 2ux

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Math

Calculus

Derivative