# How do you differentiate #y = (cos 7x)^x#?

This is nasty.

Returning to the original equation:

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To differentiate y = (cos 7x)^x, you can use the chain rule. The derivative can be calculated as follows:

y' = (cos 7x)^x * [x * (cos 7x)^(x-1) * (-sin 7x) * 7 + (cos 7x)^x * ln(cos 7x)]

y' = (cos 7x)^x * [(x * (-sin 7x) * 7 * (cos 7x)^(x-1)) + (cos 7x)^x * ln(cos 7x)]

Therefore, the derivative of y = (cos 7x)^x is:

y' = (cos 7x)^x * [(x * (-7sin 7x * cos 7x)) + (ln(cos 7x))]

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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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