Question

if y=x^x sinx then find the value of dy/dx at x=π÷2​

Answer 1

Given

$y = {x}^{x} \sin(x)$

Taking log on both sides

$log(y) = log( {x}^{x} \sin(x) ) \\log(y) = log( {x}^{x}) + log( \sin(x) ) \\ log(y) = x log(x) + log( \sin(x) )$

Differentiate with respect to x

$\frac{1}{y} \times \frac{dy}{dx} = x \times \frac{1}{x} + log(x) \times 1 + \frac{1}{ \sin(x) } \times \cos(x) \\ \frac{1}{y} \frac{dy}{dx} = 1 + log(x) + \cot(x) \\ \frac{dy}{dx} = y(1 + log(x) + \cot(x) )$

Substitute for y

$\frac{dy}{dx} = {x}^{x} \sin(x) (1 + log(x) + \cot(x) )$

Sorry Bro I can't find at x=Pi/2

Pls mark as Brainliest

Answer 2

Explanation:

dy/dx=sin x ××^2+x^x ×cos x

at x=90°

=1×x^2+0

=x^2