Question

What is the derivative of `ln(sinx^2)`?

Answer 1

`2xcot(x^2)`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(x))" then "`

`dy/dx=f'(g(x))xxg'(x)larr" chain rule"`

`"here "y=ln(sin(x^2))`

`rArrdy/dx=1/(sin(x^2))xxd/dx(sin(x^2))`

`color(white)(rArrdy/dx)=1/(sin(x^2))xxcos(x^2)xxd/dx(x^2)`

`color(white)(rArrdy/dx)=cos(x^2)/sin(x^2)xx2x`

`color(white)(rArrdy/dx)=2xcot(x^2)`