Question

diffrentitate x^sinx .w.r.t.x.

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Answer 1

$y = {x}^{sinx}$

Taking log both sides

$logy = sinx \times logx$

Apply differentiation

$\frac{1}{y} \frac{dy}{dx} = sinx \frac{d}{dx} (logx) + logx \frac{d}{dx} (sinx)$

$\frac{1}{y} \frac{dy}{dx} = sinx( \frac{1}{x} ) + logxcosx$

$\frac{dy}{dx} = y( \frac{sinx}{x} + logxcosx)$

$\frac{dy}{dx} = {x}^{sinx} ( \frac{sinx}{x} + logxcosx)$

Please mark me brainliest if my answer was correct.