Calculus Help?

Question

1) Let f and g dentote differentiable funcions such that

f(1)= pi, f'(1)=5
g(1)= 3, g'(1)=0

find h'(1) where

h(t)=sin [ f(t) g(t)]


2) find the slope of the tangent line to the curve

sin(xy)=x

at the point

(1, pi/2)

3. Find the exact coordinates of the point (x,y) where the tangent line to the graph of

y^3 - xy=-6

is vertical.

Answer 1

1) h(t) = sin [f(t)g(t)]

[f(t)g(t)]'cos[f(t)g(t)]

[f'(t)g(t) + f(t)g'(t)]cos[f(t)g(t)]

[f'(1)g(1) + f(1)g'(1)]cos[f(1)g(1)]

[5 + 0]cos[3pi]

5cos(3pi)

-5