Question

if y = x^x Then dy/dx = ?​

Answer 1

y = x^x

dy/dx= x^x(1+log x)

Treat this term as x^n and a^x...then this answer will come..hope it helps,please follow me thanks ❤.

=>x(x)^x-1 + x^x(logx)

=>x^x(1+log x)

Answer 2

$\huge{ \mathtt{ \fbox{Solution :}}}$

Given ,

$\sf \star \: \: y = {(x)}^{x}$

To find ,

$\sf \star \: \frac{dy}{dx} = \: ?$

Thus ,

$\sf \hookrightarrow \frac{d {(x)}^{x} }{dy} \\ \\ \sf \hookrightarrow x {(x)}^{x - 1} \: \: \: \{ \: \: \because \frac{d {(x)}^{n} }{dx} = n {(x)}^{n - 1} \: \: \} \\ \\ \sf \hookrightarrow {(x)}^{x - 1 + 1}\\ \\\sf \hookrightarrow {(x)}^{x}$

Hence , the differentiation of (x)^x with respect to x is (x)^x