How do you differentiate #f(x)=4x ln(3sin^2x^2 + 2)# using the chain rule?

1 Answer
Nov 6, 2015

Answer:

#f'(x)=4ln(3sin^2x^2+2) + (48x^2cosx^2)/(3sin^2x^2+2)#

Explanation:

#f'(x)=(4x)' * ln(3sin^2x^2+2) + 4x * (ln(3sin^2x^2+2))'#

#f'(x)=4ln(3sin^2x^2+2) + 4x * 1/(3sin^2x^2+2) * (3sin^2x^2+2)'#

#f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * (3sin^2x^2)'+0#

#f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * 6(sinx^2)'#

#f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * 6cosx^2 * (x^2)'#

#f'(x)=4ln(3sin^2x^2+2) + (4x)/(3sin^2x^2+2) * 6cosx^2 * 2x#

#f'(x)=4ln(3sin^2x^2+2) + (48x^2cosx^2)/(3sin^2x^2+2)#