Question

If y= tan^-x then find d^2y /dx^2 in terms of y alone

Answer 1

Answer:

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Answer 2

ANSWER:-

$\sf\blue{Given\:that\:y={x}^{3}+tan\:x.Then}$

$\longrightarrow$$\sf\red{ \frac{dy}{dx} = {3x}^{2} + {sec}^{2}x }$

$\longrightarrow$$\sf\red{\frac{ {d}^{2} y}{ {dx}^{2} } = \frac{d}{dx} ( {3x}^{2} + {sec}^{2} x)}$

$\longrightarrow$$\sf\red{6x + 2 \: sec \: x. \: sec \: x \: tan \: x }$

$\longrightarrow$$\sf\red{6x + 2 {sec}^{2} \: x \: tan \: x}$