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

Answer 1

Answer :

#y'=e^(-kx)(1-k*x)#

Solution :

Suppose :

#y=f(x)*g(x)#

Using Product Rule which is,

#y'=f(x)*g'(x)+f'(x)*g(x)#

Similarly following for the given problem,

#y=x*e^(-kx)#
Differentiating with respect to #x#,
#y'=x*(e^(-kx))'+e^(-kx)*(x)'#
#y'=x*(-k*e^(-kx))+e^(-kx)#
#y'=e^(-kx)(1-k*x)#
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Answer 2

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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Answer from HIX Tutor

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.

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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