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 2101 views around the world You can reuse this answer Creative Commons License