Question

If y=cos{log(x^n)}, find dy/dx

Answer 1

Answer:

dy/dx = [-n.sin{log(x^n)}]/x

Step-by-step explanation:

Let log(x^n) = u.

=> dy/du = sin(u) = -sin{log(x^n)} ........(i)

=> du/dx = 1/u = 1/x^n ..........................(ii)

and, d(x^n)/dx = nx^(n-1) ......................(iii)

Multiply (i), (ii) and (iii),

dy/dx = -sin{log(x^n).1/x^n.nx^(n-1)

= -sin{log(x^n)}.nx^-1

= [-n.sin{log(x^n)}]/x