Question

d/dx eˣ log ˣ=..........,Select Proper option from the given options.
(a) xˣ(1+logx)
(b) xˣ
(c) 1+logx
(d) xˣ⁻¹

Answer 1

we have to find the value of $\frac{d}{dx}e^{xlogx}$

$e^{xlogx}$ can be written as $x^x$

now, $\frac{d}{dx}e^{xlogx}=e^{xlogx}\frac{d\{xlogx\}}{dx}\\\\=x^x[x\frac{d(logx)}{dx}+logx\frac{dx}{dx}]\\\\=x^x[x.\frac{1}{x}+logx.\frac{1}{1}]\\\\=x^x[1+logx]$

hence, answer is x^x(1 + logx)
therefore option (a) is correct

Answer 2

In the attachment I have answered this problem.

I have applied logarithmic differentiation to find derivative of the given function.

See the attachment for detailed solution.