# How do you find the derivative of the function: #(arccos(x/6))^2#?

Let

Let

Let

To differentiate, use the chain rule with a function nested within a function within a function.

The chain rule with a function nested within a function within a function:

Substituting into equation [1]

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To find the derivative of the function ( (arccos(\frac{x}{6}))^2 ), we can use the chain rule. The derivative is:

[ \frac{d}{dx} [(arccos(\frac{x}{6}))^2] = 2 \cdot arccos(\frac{x}{6}) \cdot \frac{-1}{\sqrt{1 - (\frac{x}{6})^2}} \cdot \frac{1}{6} ]

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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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