Question

find dy/dx if, y=log(x.e^x)​

Answer 1

Answer:

1/x + 1 will be the answer

Answer 2

Answer:

$\frac{1}{x} + 1$

Step-by-step explanation:

The given that,

y = log(x.e^x)

To find the dy/dx.

So,

by using formula,

$1) \: \frac{d(log \: x)}{dx} = \frac{1}{x}$

$\frac{dy}{dx} = \frac{d(log \: (x. {e}^{x} )}{dx} \\ = \frac{1}{(x. {e}^{x}) } . \frac{d(x. {e}^{x}) }{dx} \\ = \frac{1}{(x. {e}^{x}) } .1. {e}^{x} + x. {e}^{x} \\ = \frac{ {e}^{x} }{x. {e}^{x} } + \frac{x {e}^{x} }{x {e}^{x} } \\ = \frac{1}{x} + 1$

Therefore the answer is ,( 1/x + 1 )

THANKS.