If , show…

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

17. If

y=\left(\tan ^{-1} x\right)^{2}

, show that

\left(x^{2}+1\right)^{2} y_{2}+2 x\left(x^{2}+1\right) y_{1}=2

Related theory

Higher-Order Derivatives
Advanced Differentiation
Second order derivatives
Derivatives of inverse trigonometric functions
Continuity and Differentiability

Browse the problem library