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What is the derivative of #x^sin(x)#?

Answer 1

Christopher Allers

#f'(x)=e^(sin(x))*cos(x)#

After the chain rule

#(f(g(x))'=f'(g(x))*g'(x)#

we get

#f'(x)=e^(sin(x))*cos(x)#

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Answer 2

Axel Alvarez

The derivative of ( x^{\sin(x)} ) with respect to ( x ) is given by:

[ \frac{d}{dx} \left( x^{\sin(x)} \right) = x^{\sin(x)} \left( \frac{d}{dx}(\sin(x) \ln(x)) + \frac{\sin(x)}{x} \right) ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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