Try and solve this: Calculus Derivative Problem...

Question

Determine the derivative of each a & b...

a.) You are given f(3) = -5, f '(3) = 6, g(3) = 4, and g'(3) = 8. Determine d/dx( f(x)/g(x) ) at x=3...

b.) You are given y(9) = 4 and d/dx( ln(y) ) = -3 at x=9. Determine dy/dx at x=9...

Any help is appreciated...

-Pippi A.

Answer 1

(a)

quotient rule says:

g f' - f g' / g^2

(4*6 - -5*8)/ (4^2)

(24 - -40)/16

66/16

33/8

(b) y = f(x)

f(9) = 4

G(x)= ln y = ln f(x)

G'(x)= dG/dx = f'(x) / f(x)

-3 = f'(9)/f(9)

-3 = f'(9) / 4

12 = f'(9) = dy/dx