# How do you find the derivative of #y=e^(-2x-1) * ln(-2x-1)#?

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To find the derivative of ( y = e^{-2x-1} \cdot \ln(-2x-1) ), you can use the product rule of differentiation, which states that the derivative of the product of two functions ( u ) and ( v ) is given by ( u'v + uv' ), where ( u' ) and ( v' ) are the derivatives of ( u ) and ( v ) respectively.

Let's denote ( u = e^{-2x-1} ) and ( v = \ln(-2x-1) ). The derivatives are ( u' = -2e^{-2x-1} ) and ( v' = \frac{-2}{-2x-1} ).

Now, apply the product rule:

[ y' = u'v + uv' ] [ y' = (-2e^{-2x-1}) \cdot \ln(-2x-1) + e^{-2x-1} \cdot \frac{-2}{-2x-1} ]

Simplify and factor out common terms if possible.

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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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