# How do you find the derivate for #y = pisinx - 4cosx#?

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To find the derivative of ( y = \pi \sin(x) - 4 \cos(x) ), apply the derivative rules for trigonometric functions:

[ \frac{d}{dx}(\sin(x)) = \cos(x) ] [ \frac{d}{dx}(\cos(x)) = -\sin(x) ]

Using these rules:

[ \frac{d}{dx}(\pi \sin(x)) = \pi \cos(x) ] [ \frac{d}{dx}(-4 \cos(x)) = 4 \sin(x) ]

Therefore, the derivative of ( y ) with respect to ( x ) is:

[ \frac{dy}{dx} = \pi \cos(x) + 4 \sin(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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