# What is the derivative of #y = x^cos(x)#?

Take the natural logarithm of both sides.

Hopefully this helps!

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You can write:

so:

using the chain rule:

then the product rule:

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To find the derivative of y = x^cos(x), we can use the chain rule.

First, we differentiate the exponent and then multiply it by the derivative of the base function.

The derivative of cos(x) is -sin(x), and the derivative of x^u where u is a function of x is given by u' * x^(u-1).

So, applying the chain rule, the derivative of y = x^cos(x) is:

dy/dx = cos(x) * x^(cos(x) - 1) - x^cos(x) * ln(x) * sin(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.

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