Question

Calc help!

Suppose that

f(5) = 2, f '(5) = 9, g(5) = −6, and g'(5) = 7.

Find the following values.

(fg)'(5) =

(f/g)'(5) =

(g/f)'(5)=

Answer 1

(fg)'(5) = -40

(f/g)'(5) = -68/36

(g/f)'(5)= 17

Explanation:

(fg)'(5) =

Applying the product derivative:

`fg(5) = f^(\prime)(5)g(5) + g^(\prime)(5)f(5) = 9*(-6) + 7*2 = -54 + 14 = -40`

(f/g)'(5) =

Applying the quotient derivative

`((f)/(g))^(\prime)(5) = (f^(\prime)(5)g(5) - g^(\prime)(5)f(5))/(g(5)^2) = (9*(-6) - 7*2)/(6^2) = -(68)/(36)`

(g/f)'(5)=

`((g)/(f))^(\prime)(5) = (g^(\prime)(5)f(5) - f^(\prime)(5)g(5))/(f^(\prime)(5)^2) = (7*2 - 9*(-6))/(2^2) = (68)/(4) = 17`