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What is the derivative of #sinx - (1/3)sinx^3#?

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Jim G. Share
Jun 23, 2018

Answer:

#cosx-x^2cosx^3#

Explanation:

#"differentiate "sinx^3" using the "color(blue)"chain rule"#

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

#dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"#

#d/dx(sinx^3)=cosx^3xxd/dx(x^3)=3x^2cosx^3#

#rArrd/dx(sinx-1/3sinx^3)#

#=cosx-1/3xx3x^2cosx^3#

#=cosx-x^2cosx^3#

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