How do you differentiate y = sin (ln(x)^2+2) using the chain rule?

1 Answer
Jul 30, 2018

(dy)/(dx)=2/xlnx cos(ln(x)^2+2)

Explanation:

Here ,

y=sin(ln(x)^2+2)

Let , y=sinu , where, color(red)(u=ln(x)^2+2

=>(dy)/(du)=cosu and (du)/(dx)=2lnx*1/x=2/xlnx

Using Chain Rule:

color(blue)((dy)/(dx)=(dy)/(du)*(du)/(dx)

:.(dy)/(dx)=cosu xx 2/xlnx=2/xlnxcosu

Subst. color(red)(u=ln(x)^2+2

:.(dy)/(dx)=2/xlnx cos(ln(x)^2+2)