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

1 Answer
Dec 28, 2015

Answer:

Step by step explanation and working is given below.

Explanation:

#f(x)=ln(3x^2)#

For chain rule, first break the problem into smaller links and find their derivatives. The final answer would be the product of all the derivatives in the link.

#y=ln(u)#
#u=3x^2#

The differentiation using chain rule would be

#dy/dx = dy/(du) * (du)/(dx)#

#y=ln(u)#
Differentiate with respect to #u#

#dy/(du) = 1/u #

#u=3x^2#
Differentiate with respect to #x#
#(du)/(dx) = 3(d(x^2))/dx#
#(du)/(dx) = 3*2x#
#(du)/(dx)=6x#

#dy/dx = 1/u*6x#
#dy/dx = (6x)/u#

#dy/dx = (6x)/(3x^2)#

#dy/dx = 2/x# Final answer

Note: The above process might look big, this was given in such a form to help you understand step by step working. With practice, you can do it quickly and with less steps.