Product & Quotient #16

Question

Suppose that  and  and let  and  Answer the following questions.

1. Find 

Answer:  2. Find 

Answer:  

Answer 1

Use the product rule for g(x) and the quotient rule for h(x).

The product rule says for u•v, (u•v)' = u'v + uv' so:

g'(x) = f '(x)•sin(x) + f(x)•(sin(x))'

You've been taught what the derivative of sin(x) is, so just use that and plug in x = π/3

The quotient rule says for (u/v) that (u/v)' = (u'v - uv')/v²

u = cos(x) and v = f(x)

u' = -sin(x) and v' = f '(x)

v² = (f(x))²

Just plug and chug.