First slide

Diffrentiation

Question

$If y = x l nx then \frac{d y}{d x} will be$

Moderate

A

$l n x + x$
B

$1 + l n x$
C

$l n x$
D

$1$

Solution

$\begin{array}{l} y = x \log x \\ \frac{d y}{d x} = \frac{x d \log x}{d x} + \log x \frac{d x}{d x} \\ = x (\frac{1}{x}) + \log (x) (1) (∵ \frac{d}{d x} \log x = \frac{1}{x} \frac{d x}{d x} = 1) \\ = 1 + \log x \end{array}$

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