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e^-x
The derivative of the function/ e^-x

Derivative of e^-x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -x
e
e−xe^{- x} 
d / -x\
--\e  /
dx
ddxe−x\frac{d}{d x} e^{- x}
Transform
Detail solution

  1. Let u=−xu = - x.

  2. The derivative of eue^{u} is itself.

  3. Then, apply the chain rule. Multiply by ddx(−x)\frac{d}{d x} \left(- x\right):

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: xx goes to 11

      So, the result is: −1-1

    The result of the chain rule is:

    −e−x- e^{- x}

The answer is:

−e−x- e^{- x}

The graph
02468-8-6-4-2-1010-5000050000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  -x
-e
−e−x- e^{- x}
Simplify
The second derivative [src] 
 -x
e
e−xe^{- x}
Simplify
The third derivative [src] 
  -x
-e
−e−x- e^{- x}
Simplify
The graph
Derivative of e^-x
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