# How do you find the derivative of #y=x cosx #?

Apply the rule of the product:

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To find the derivative of ( y = x \cos(x) ), you can use the product rule of differentiation, which states that the derivative of a product of two functions is the derivative of the first function times the second function, plus the first function times the derivative of the second function.

Using the product rule, the derivative of ( y = x \cos(x) ) is:

[ \frac{dy}{dx} = \frac{d}{dx}(x) \cdot \cos(x) + x \cdot \frac{d}{dx}(\cos(x)) ]

Applying the derivative of ( x ) and ( \cos(x) ), we get:

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

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