# How do you find the derivative of #y=e^x cos(x)# ?

which is the necessary resolution.

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This kind of issue is one that makes use of the product rule.

According to the product rule:

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To find the derivative of ( y = e^x \cos(x) ), you can use the product rule of differentiation, which states that if ( u ) and ( v ) are differentiable functions of ( x ), then the derivative of their product is given by ( (uv)' = u'v + uv' ). Applying this rule:

[ \frac{d}{dx}(e^x \cos(x)) = e^x \cdot (-\sin(x)) + \cos(x) \cdot e^x ]

So, the derivative of ( y = e^x \cos(x) ) is:

[ y' = e^x \cdot (-\sin(x)) + \cos(x) \cdot e^x = e^x (-\sin(x) + \cos(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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