Method of Differentiation
Implicit Differentiation
Premium Question
Grade 12
Question:
If $y = (\tan^{-1} x)^2$, the value of $(1 + x^2)^2 y'' + 2x(1 + x^2)y'$ (which is independent of $x$) equals _____.
Step-by-Step Solution
Key Concept: First multiply the relation $y' = \frac{2 \tan^{-1} x}{1 + x^2}$ throughout by $(1 + x^2)$ to get a clean intermediate equation, then differentiate that equation once more.
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Correct Answer: 2