How can I find the derivative of this? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Shwetank Mauria Mar 18, 2017 #(d^2y)/(dx^2)=6xcosx-6x^2sinx-x^3cosx# Explanation: 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# Answer link Related questions What is the derivative of #f(x)=sin^-1(x)# ? What is the derivative of #f(x)=cos^-1(x)# ? What is the derivative of #f(x)=tan^-1(x)# ? What is the derivative of #f(x)=sec^-1(x)# ? What is the derivative of #f(x)=csc^-1(x)# ? What is the derivative of #f(x)=cot^-1(x)# ? What is the derivative of #f(x)=(cos^-1(x))/x# ? What is the derivative of #f(x)=tan^-1(e^x)# ? What is the derivative of #f(x)=cos^-1(x^3)# ? What is the derivative of #f(x)=ln(sin^-1(x))# ? See all questions in Differentiating Inverse Trigonometric Functions Impact of this question 1067 views around the world You can reuse this answer Creative Commons License