# How do you differentiate #y = 6sin cos4x#?

-24 cos cos4x. sin 4x

Applying the chain rule makes this task simple: as demonstrated below, y' = 6 cos cos4x.(-sin4x). First, differentiate sin with respect to cos 4x; next, differentiate cos with respect to 4x; and finally, differentiate 4x with respect to x.

= -24 sin 4x. cos cos 4x

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To differentiate ( y = 6\sin(x)\cos^4(x) ), you can use the product rule. Let ( u = \sin(x) ) and ( v = \cos^4(x) ). Then, ( \frac{du}{dx} = \cos(x) ) and ( \frac{dv}{dx} = -4\cos^3(x)\sin(x) ). Apply the product rule: ( \frac{dy}{dx} = u'\cdot v + u \cdot v' ). Finally, substitute the derivatives and simplify to find the result.

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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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