009A Sample Midterm 2, Problem 5

Find the derivatives of the following functions. Do not simplify.

a) $f(x)=\tan ^{3}(7x^{2}+5)$

b) $g(x)=\sin(\cos(e^{x}))$

c) $h(x)={\frac {(5x^{2}+7x)^{3}}{\ln(x^{2}+1)}}$

Foundations:
1. Chain Rule
2. Derivatives of trig/ln
3. Quotient Rule

Solution:

(a)

Step 1:
First, we use the Chain Rule to get
<math>f'(x)=3\tan^2(

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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