Find the derivative of Cubic Root of x^2+5x+2. Better Formulated : [x^2+5x+2]^1/3How to find the Derivative, is there any rule i have to follow to find derivatives for such functions.

Expert Answers
justaguide eNotes educator| Certified Educator

The derivative of f(x) = `(x^2+5x+2)^(1/3)` has to be derived. Use the chain rule: if h(x) = g(f(x)), h'(x) = g'(f(x))*f'(x)

For f(x) = (x^2+5x+2)^(1/3)

f'(x) = `(1/3)*(x^2+5x+2)^(-2/3)*(2x + 5)`

The required derivative is `(2x + 5)/(3*(x^2+5x+2)^(2/3))`