# How do you use the chain rule to differentiate #y=cos(sqrt(8t+11))#?

Answer is

Differentiating y with respect to t.

Using Chain Rule

Let g =

New expression will be

Using

Using

and also put g= 8t+11 in place of g in equation (2)

On simplifying

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To differentiate ( y = \cos(\sqrt{8t + 11}) ) using the chain rule, follow these steps:

- Identify the outer function: ( \cos(u) ), where ( u = \sqrt{8t + 11} ).
- Differentiate the outer function with respect to its inner variable: ( \frac{d}{du}\left[\cos(u)\right] = -\sin(u) ).
- Identify the inner function: ( u = \sqrt{8t + 11} ).
- Differentiate the inner function with respect to ( t ): ( \frac{du}{dt} = \frac{1}{2\sqrt{8t + 11}} ).
- Apply the chain rule: ( \frac{dy}{dt} = -\sin(\sqrt{8t + 11}) \cdot \frac{1}{2\sqrt{8t + 11}} ).
- Simplify the expression if necessary.

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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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