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

1 Answer
Jim G.
Sep 25, 2017

#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)#

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