What's the derivative of #y= arctan(sqrtx)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Michael Mar 15, 2016 #f'(x)=(1)/(2sqrt(x)(x+1)# Explanation: #f(x)=arctan(sqrt(x))# Apply the chain rule: #f'(x)=(1)/(x+1).(dsqrt((x)))/(dx)# #f'(x)=((1)/(2sqrt(x)))/((x+1))# #f'(x)=(1)/(2sqrt(x)(x+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 2288 views around the world You can reuse this answer Creative Commons License