What is the derivative of #ln(sinx^2)#?
1 Answer
Sep 25, 2017
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)#
