How do you use the chain rule to differentiate f(x)=sqrt(4x^3+6x)?

2 Answers
May 14, 2017

f'(x) = (6x^2+3)/sqrt(4x^3+6x)

Explanation:

Differentiate of x |-> 4x^3+6x is 4*3x^2+6*1 = 12x^2+6
and differentiate of x |-> sqrt(x) is 1/(2sqrt x)

Hence by applying the formula (f(g))' = g'*f'(g),

f'(x) = (12x^2+6)*1/(2*sqrt(4x^3+6x)

=> f'(x) = (6x^2+3)/sqrt(4x^3+6x)

May 14, 2017

(6x^2+3)/(sqrt(4x^3+6x))

Explanation:

d/dx[sqrt(4x^3+6x)]=(d/dx[(4x^4+6x)^(1/2)])(d/dx[4x^3+6x])=(1/2)(4x^3+6x)^(1/2-1)(12x^2+6)=(12x^2+6)/(2sqrt(4x^3+6x))=(6x^2+3)/(sqrt(4x^3+6x))