y= x(log x)^2 + 1 dydx = 1.(1+ (log x)^2_) (2log x×1x)x(1+(log x)^2_)^2_ dydx = (1 log x)^2_(1+(log x)^2)^2_ ...

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Chain Rule of Differentiation

ddx xlogx2 +...

Question

$\frac{d}{d x} (\frac{x}{log x^{2} + 1})$

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Solution

$y = \frac{x}{(log x)^{2} + 1}$
$\frac{d y}{d x} = \frac{1. (1 + (log x)^{2}) - (2 log x \times \frac{1}{x}) x}{(1 + (log x)^{2})^{2}}$
$\frac{d y}{d x} = \frac{(1 - log x)^{2}}{(1 + (log x)^{2})^{2}}$

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