Question

How do you differentiate `f(x)=sqrt(xsin(ln(x)^3)` using the chain rule?

Answer 1

`(sinlnx^3+3coslnx^3)/(2sqrt(xsinlnx^3))`

Explanation:

`f'(x)=1/(2sqrt(xsinlnx^3))*(1*sinlnx^3+cancelx*coslnx^3*1/cancel(x^3)*3cancel(x^2))`

`=(sinlnx^3+3coslnx^3)/(2sqrt(xsinlnx^3))`