How do you differentiate #f(x)=-x^3*(-5sinx)# using the product rule?

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Answer 1 · 2015-11-27T17:55:27

#f'(x)=5x^3cosx+15x^2sinx#

The product rule states that:

#d((uv))/dx=v.(du)/dx+u.(dv)/dx#

#f(x)=-x^3.(-5sinx)#

This simplifies to:

#f(x)=5x^3.sinx#

#:.f'(x)=5(x^3cosx+3x^2sinx)#

#f'(x)=5x^3cosx+15x^2sinx#