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How do you find the derivative of #2e^-x#?

Answer 1

Luke Alvarez

#(dy)/(dx)=-2e^-x#

Recall that #d/dxe^x=e^x#

Using chain rule, #(dy)/(dx)=(dy)/(du)*(du)/(dx)#,

Let #u=-x#

#(dy)/(du)=d/(du)2e^u=2e^u=2e^-x#

#(du)/(dx)=d/(dx)-x=-1#

#:.(dy)/(dx)=-1*2e^-x=-2e^-x#

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Answer 2

Axel Alvarez

To find the derivative of ( 2e^{-x} ), apply the chain rule. The derivative of ( e^{-x} ) is ( -e^{-x} ). Multiply this by the derivative of the outer function, which is 2. So, the derivative of ( 2e^{-x} ) is ( -2e^{-x} ).

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Answer 3

Isaiah Allen

To find the derivative of (2e^{-x}):

The derivative of (e^u) with respect to (x) is (\frac{d}{dx}(e^u) = e^u \cdot \frac{du}{dx}).

In this case, (u = -x). Therefore, (\frac{du}{dx} = -1).

Now, substitute (u = -x) and (\frac{du}{dx} = -1) into the derivative formula:

(\frac{d}{dx}(2e^{-x}) = 2 \cdot e^{-x} \cdot (-1))

(\frac{d}{dx}(2e^{-x}) = -2e^{-x})

So, the derivative of (2e^{-x}) with respect to (x) is (-2e^{-x}).

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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.