How do you differentiate #f (x) = 3 arcsin (x^4)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Shiva Prakash M V Mar 31, 2018 #dy/dx=(12x^3)/sqrt(1-x^8)# Explanation: #f(x)=3arcsin(x^4)# Let #y=f(x)# #3arcsin(x^4)=3sin^-1(x^4)# #y=3sin^-1(x^4)# Let #u=x^4# #y=3sin^-1u# By chain rule #dy/dx=dy/(du).(du)/dx# #y=3sin^-1u# #dy/(du)=3xx1/sqrt(1-u^2)# #u=x^4# #u^2=(x^4)^2# #u^2=x^8# #dy/(du)=3/sqrt(1-x^8)# #u=x^4# #(du)/dx=4x^3# #dy/dx=dy/(du).(du)/dx# #dy/dx=(3/sqrt(1-x^8)).(4x^3)# #dy/dx=(12x^3)/sqrt(1-x^8)# 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 1881 views around the world You can reuse this answer Creative Commons License