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Higher Order Derivatives

If y=tan x,...

Question

If $y = tan x$ , prove that $y_{2} = 2 y y_{1}$ .

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Solution

$y = tan x$

$∴ \frac{d y}{d x} = y_{1} = {sec}^{2} x$

$\frac{d}{d x} (y_{1}) = y_{2} = 2 sec x \frac{d}{d x} (sec x)$

$y_{2} = 2 {sec}^{2} x tan x$

$y_{2} = 2 y y_{1}$

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