009A Sample Midterm 1, Problem 4

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

a) $f(x)={\sqrt {x}}(x^{2}+2)$

b) $g(x)={\frac {x+3}{x^{\frac {3}{2}}+2}}$ where $x>0$

c) $h(x)={\frac {e^{-5x^{3}}}{\sqrt {x^{2}+1}}}$

Foundations:
1. Product Rule
2. Quotient Rule
3. Chain Rule

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

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

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