Question

Explique passo a passo como Derivas esta função:

f (x): 3 √(ln x^3)

Answer 1

u=x³

v= ln u

w=√v

f'(x)= 3 *  w'  *  v'  * u'

f'(x) = 3 * (1/2) * v^(-1/2)  * (1/u)  *  (3x²)

****v= ln u
****u=x³

f'(x) = 3 * (1/2) * (ln u)^(-1/2)  * (1/x³)  *  (3x²)

f'(x) = 3 * (1/2) * (ln x³)^(-1/2)  * (1/x³)  *  (3x²)

f'(x) = 3 * (1/2) * (1/(√ln x³) * (1/x³)  *  (3x²)

f'(x) = 3 * (1/2) * (1/(√ln x³) * (3/x)

f'(x) = (9/2x) * (1/(√ln x³) 

f'(x) =9/[2x√(ln x³)]