What is the Derivative of y=sin²x² ?
3 Answers
Explanation:
We know that,
Here,
Explanation:
#"differentiate using the "color(blue)"chain rule"#
#"Given "y=f(g(x))" then"#
#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#
#y=sin^2x^2=(sinx^2)^2#
#rArrdy/dx=2sinx^2xxd/dx(sinx^2)#
#color(white)(rArrdy/dx)=2sinx^2xxcosx^2xxd/dx(x^2)#
#color(white)(rArrdy/dx)=4xsinx^2cosx^2=2xsin2x^2#
Explanation:
Where:
Apply chain rule:
Therefore,
Using following identity: