What is the derivative of #arctan (x/2)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Shwetank Mauria Jun 26, 2016 #(dy)/(dx)=1/2cos^2(arctan(x/2))# Explanation: As #y=arctan(x/2)# #tany=x/2# Hence, #sec^2yxx(dy)/(dx)=1/2# or #(dy)/(dx)=1/2cos^2y=1/2cos^2(arctan(x/2))# 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 1083 views around the world You can reuse this answer Creative Commons License