How do you differentiate y=sec^-1(x^2)y=sec−1(x2)? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer sjc Jan 4, 2017 (dy)/(dx)=2/(xsqrt(x^4-1))dydx=2x√x4−1 Explanation: y=sec^(-1)x^2y=sec−1x2 =>x^2=secy⇒x2=secy differentiate wrt xx 2x=(dy)/(dx)secytany2x=dydxsecytany (dy)/(dx)=(2x)/(secytany)dydx=2xsecytany now substitute back using: secy=x^2secy=x2 sec^2y=1+tan^2y=>tany=sqrt(sec^2y-1sec2y=1+tan2y⇒tany=√sec2y−1 tany=sqrt(x^4-1)tany=√x4−1 (dy)/(dx)=(2x)/(x^2sqrt(x^4-1))=2/(xsqrt(x^4-1))dydx=2xx2√x4−1=2x√x4−1 Answer link Related questions What is the derivative of f(x)=sin^-1(x)f(x)=sin−1(x) ? What is the derivative of f(x)=cos^-1(x)f(x)=cos−1(x) ? What is the derivative of f(x)=tan^-1(x)f(x)=tan−1(x) ? What is the derivative of f(x)=sec^-1(x)f(x)=sec−1(x) ? What is the derivative of f(x)=csc^-1(x)f(x)=csc−1(x) ? What is the derivative of f(x)=cot^-1(x)f(x)=cot−1(x) ? What is the derivative of f(x)=(cos^-1(x))/xf(x)=cos−1(x)x ? What is the derivative of f(x)=tan^-1(e^x)f(x)=tan−1(ex) ? What is the derivative of f(x)=cos^-1(x^3)f(x)=cos−1(x3) ? What is the derivative of f(x)=ln(sin^-1(x))f(x)=ln(sin−1(x)) ? See all questions in Differentiating Inverse Trigonometric Functions Impact of this question 7749 views around the world You can reuse this answer Creative Commons License