What is the derivative of tan^-1(4x)? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 2 Answers bp Apr 23, 2015 4/(16x^2 +1) Derivative of tan^-1 4x can be written using the formula for the derivative of tan^-1x = 1/(1+x^2) d/dx tan^-1 4x = 1/(16x^2 +1) d/dx (4x) = 4/(16x^2 +1) Answer link Tiago Hands Apr 23, 2015 y=arctan(4x) tany=4x sec^2y*(dy)/(dx)=4 (tan^2y+1)*(dy)/(dx)=4 (16x^2+1)*(dy)/(dx)=4 (dy)/(dx)=4/(16x^2+1) 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 22170 views around the world You can reuse this answer Creative Commons License