Find f'(x) in the following problem

Question

f(x) = 10 ⁴√x³ + 5/ x² + (ln 2)²

find f' (x)

Answer 1

It will help to write these with fractional exponents as much as possible

(10)(x^3/4) +5x^-2 + (ln2)^2 Now can take the derivative

(10)(3/4)( x^-1/4) +(5)(-2)(x^-3) + 2(ln2)^2[this last term is a constant so it’s derivative is 0]

7.5(x^-1/4) -10x^-3 + 0= 7.5(x^-1/4) -10x^-3