Question

given f(7)=4, f'(7)=10, g(7)=-1, g'(7)=8, find the values of the following: 1. (fg)'(7) = 2. (f/g)'(7) =

Answer 1

By the product rule,

`(fg)'=f'g+fg'`

so that

`(fg)'(7)=f'(7)g(7)+f(7)g'(7)=10\cdot(-1)+4\cdot8=22`

By the quotient rule,

`\left(\frac fg\right)'=(f'g-fg')/(g^2)`

so that

`\left(\frac fg\right)'(7)=(f'(7)g(7)-f(7)g'(7))/(g(7)^2)=(10\cdot(-1)-4\cdot8)/((-1)^2)=-42`