Find F'(x) and f''(x)

Question

f(x)= x^2/ 7+4x

Find f'(x) and f''(x)

Answer 1

Hi Nicole,

We will use the quotient rule to take the derivative of this fraction.

if f(x)=h(x)/g(x) then f'(x) = [g(x)*h'(x) - g'(x)*h(x)]/(g(x))²

so in this case f(x)= x²/(7+4x) where h(x)=x² so h'(x)=2x and g(x)=7+4x so g'(x)=4

now we can plug those into the quotient rule and find that

f'(x) = [(7+4x)*(2x) - (4)*(x²)] / (7+4x)²

This can be simplified. Then by repeating the same process you can find f''(x) (:

goodluck!