Calculus: Chain Rule!!!!!!!!!!!!!!!!!!!!

Question

Calculate

d/dx(e^(sin^2(1/x)))

Answer 1

y=e^(sin^2(1/x)))

Take logarthim both sides

y=e^(sin^2(1/x)))

lny=sin^2(1/x)

Take derivative both sides

(1/y)dy/dx=2sin(1/x)cos(1/x)*(-1/x^2)

dy/dx=-y/x^2sin(2/x)

       =-e^(sin^2(1/x)))sin(2/x)/x^2