What is the derivative of #x^sin(x)#?
Take the natural logarithm of both sides.
Use laws of logarithms to simplify.
Use the product rule and implicit differentiation to differentiate.
Hopefully this helps!
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Use logarithmic differentiation.
Use implicit differentiation on the left side:
Use the product rule on the right sides:
Substituting into the product rule:
Put the equation back together:
Multiply both sides by y:
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The derivative of ( x^{\sin(x)} ) with respect to ( x ) is given by ( x^{\sin(x)}(\ln(x)\cos(x)+\frac{\sin(x)}{x}) ).
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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.
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.
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.
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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