How do you differentiate #y=cos^-1(-5x^3)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Monzur R. Jan 10, 2018 #dy/dx = (15x^2)/sqrt(1-25x^6)# Explanation: The derivative of #cos^-1(u) = -(u^')/sqrt(1-u^2)# Here the function is #y=cos^-1(-5x^3)#, so #dy/dx = -((-5x^3)^')/sqrt(1-(-5x^3)^2)=(15x^2)/sqrt(1-25x^6)# 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 2154 views around the world You can reuse this answer Creative Commons License