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How do you differentiate #y=1/e^x#?

Answer 1

To differentiate ( y = \frac{1}{e^x} ), you can use the chain rule. The derivative of ( e^x ) is ( e^x ). Applying the chain rule, the derivative of ( \frac{1}{e^x} ) with respect to ( x ) is:

[ \frac{d}{dx} \left( \frac{1}{e^x} \right) = -\frac{1}{{e^x}} \cdot \frac{d}{dx}(e^x) = -\frac{1}{e^x} \cdot e^x = -e^{-x} ]

So, the derivative of ( y = \frac{1}{e^x} ) is ( y' = -e^{-x} ).

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Answer 2

Elijah Abram

#dy/dx=-e^-x=-1/e^x#

differentiate using the #color(blue)"power rule and chain rule"#

#y=1/e^x=e^-x#

#rArrdy/dx=e^-x.d/dx(-x)=-e^-x=1/e^x#

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Answer 3

Cameron Alexander

To differentiate ( y = \frac{1}{e^x} ), you can use the chain rule.

First, rewrite the function as ( y = e^{-x} ).

Then, differentiate using the chain rule, which states that if you have a function ( f(g(x)) ), its derivative is ( f'(g(x)) \cdot g'(x) ).

So, the derivative of ( y = e^{-x} ) is:

[ \frac{dy}{dx} = -e^{-x} ]

Therefore, the derivative of ( y = \frac{1}{e^x} ) is:

[ \frac{dy}{dx} = -\frac{1}{e^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.