Question

`d/dx(x^{sinx})` = ______ 

Options

• `(sinx/x + cosx logx)`

• `x^sinx(sinx/x - cosx logx)`

• `x^sinx(sinx/x + cosx)`

• `x^sinx(sinx/x + cosx logx)`

Answer 1

`d/dx(x^{sinx})` = `underline(x^sinx(sinx/x + cosx logx))`

Explanation:

Let y = x^sinx

Taking logarithm on both sides, we get

log y = (sin x) log x

Differentiating both sides w.r.t. x, we get

`1/y . dy/dx = sinx/x + cosx logx`

∴ `dy/dx = x^sinx(sinx/x + cosx logx)`