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Provide solution for RD Sharma maths class 12 chapter Higher Order Derivatives exercise 11.1 question 26

Answers (1)

Answer:

Proved

Hint:

You must know the derivative of logarithm and tangent inverse x

Given:

y=\tan ^{-1} x, \text { show }\left(1+x^{2}\right) \frac{d^{2} y}{d x^{2}}+(2 x) \frac{d y}{d x}=\frac{d y}{d x}

Solution:

y=\tan ^{-1} x

        Di\! f\! f\! erentiate\; the\; equation\; w.r.t \; x \\ \frac{d y}{d x}=\frac{1}{1+x^{2}}\\ \left(1+x^{2}\right) \frac{d y}{d x}=1 \\ Di\! f\! f\! erentiate\; again \\ \left(1+x^{2}\right) \frac{d^{2} y}{d x^{2}}+(2 x) \frac{d y}{d x}=0 \\ or \\ \left(1+x^{2}\right) y_{2}+(2 x) y_{1}=0

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