# How do you differentiate #y=(r^2-2r)e^r#?

Apply the product rule:

So

Simplify:

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To differentiate ( y = (r^2 - 2r)e^r ), we can use the product rule of differentiation.

Let's denote ( u = r^2 - 2r ) and ( v = e^r ).

Then, the derivative of ( u ) with respect to ( r ) is ( \frac{du}{dr} = 2r - 2 ), and the derivative of ( v ) with respect to ( r ) is ( \frac{dv}{dr} = e^r ).

Now, applying the product rule:

[ \frac{dy}{dr} = \frac{du}{dr}v + u\frac{dv}{dr} ]

[ \frac{dy}{dr} = (2r - 2)e^r + (r^2 - 2r)(e^r) ]

[ \frac{dy}{dr} = 2re^r - 2e^r + r^2e^r - 2re^r ]

[ \frac{dy}{dr} = r^2e^r - 2e^r ]

So, the derivative of ( y ) with respect to ( r ) is ( r^2e^r - 2e^r ).

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