Question

differentiat x^x w.r to x^ sinx​

Answer 1

The derivative of xˣ with respect to x is

xˣ ( 1 + ln(x))

$\frac{d}{dx} ( {x}^{x} ) = \frac{d}{dx} ( {e}^{x. ln(x) } )$

$= \frac{d}{du} ( {e}^{u} ). \: \frac{d}{dx} (x. ln(x) )$

$= { {x} }^{x}( x. \frac{1}{x} + ln(x) )$

$= {x}^{ {x} } (1 + ln(x) )$

$\frac{d}{dx} ({x}^{x}) = {x}^{ {x} } + {x}^{x} . ln(x)$