What is the derivative of #cosx^3#?

1 Answer
Jim G.
Jul 7, 2016

#-3x^2sinx^3#

Explanation:

Differentiate using the #color(blue)"chain rule"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x)).g'(x))color(white)(a/a)|))....(A)#

#f(g(x))=cos(x^3)rArrf'(g(x))=-sin(x^3)#

and #g(x)=x^3rArrg'(x)=3x^2#
#"----------------------------------------------------"#
Substitute these values in #color(red)"(A)"#

#rArrd/dx(cosx^3)=-sinx^3 .3x^2=-3x^2sinx^3#

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