# How do you find the derivative of #tan^4 (x)#?

By using the power rule

and the chain rule

As a result:

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To find the derivative of ( \tan^4(x) ), you can use the chain rule.

[ \frac{d}{dx}(\tan^4(x)) = 4 \tan^3(x) \sec^2(x) ]

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To find the derivative of ( \tan^4(x) ), we can use the chain rule. First, let's rewrite ( \tan^4(x) ) as ( (\tan(x))^4 ). Then, we differentiate using the chain rule:

[ \frac{d}{dx}(\tan^4(x)) = \frac{d}{dx}((\tan(x))^4) ]

Let ( u = \tan(x) ). Then, ( \frac{du}{dx} = \sec^2(x) ).

Now, we apply the chain rule:

[ \frac{d}{dx}((\tan(x))^4) = 4(\tan(x))^3 \cdot \frac{du}{dx} ]

[ = 4\tan^3(x) \cdot \sec^2(x) ]

So, the derivative of ( \tan^4(x) ) with respect to ( x ) is ( 4\tan^3(x) \sec^2(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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