# How do you find the derivative of #f(x) = cos(pi/2)x# using the chain rule?

For the function formulated in the question, the derivative is

However, the question might have meant this derivative instead:

Thus,

======================

You might have also meant

instead.

In this case, you can apply the chain rule as follows:

It holds

Thus, your derivative is

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To find the derivative of ( f(x) = \cos\left(\frac{\pi}{2}x\right) ) using the chain rule, we first identify the outer function and the inner function. In this case, the outer function is ( \cos(x) ) and the inner function is ( \frac{\pi}{2}x ). Then, we apply the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function.

[ f'(x) = -\sin\left(\frac{\pi}{2}x\right) \cdot \frac{\pi}{2} = -\frac{\pi}{2}\sin\left(\frac{\pi}{2}x\right) ]

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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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