How can I find the derivative of this?

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Answer 1 · 2017-03-18T16:15:42

#(d^2y)/(dx^2)=6xcosx-6x^2sinx-x^3cosx#

As #y=x^3cosx#

#(dy)/(dx)=3x^2cosx+x^3(-sinx)#

= #3x^2cosx-x^3sinx#

and #(d^2y)/(dx^2)=d/(dx)((dy)/(dx))#

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

= #(6xcosx+3x^2(-sinx))-(3x^2sinx+x^3cosx)#

= #6xcosx-3x^2sinx-3x^2sinx-x^3cosx#

= #6xcosx-6x^2sinx-x^3cosx#