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

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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