# What is the derivative of #xe^(-kx)#?

Answer :

Solution :

Suppose :

Using Product Rule which is,

Similarly following for the given problem,

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The derivative of xe^(-kx) with respect to x is given by the product rule, which states that if u and v are differentiable functions of x, then the derivative of uv with respect to x is u'v + uv', where u' and v' denote the derivatives of u and v respectively.

Using the product rule, the derivative of xe^(-kx) with respect to x is:

d/dx [xe^(-kx)] = (1)e^(-kx) + x(-ke^(-kx)) = e^(-kx) - kxe^(-kx)

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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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