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Derivative of:
Derivative of sin(x)^2
Derivative of e^(2-x)
Derivative of cos(x/3)
Derivative of √x
Integral of d{x}:
e^(2-x)
Limit of the function:
e^(2-x)
Identical expressions
e^(two -x)
e to the power of (2 minus x)
e to the power of (two minus x)
e(2-x)
e2-x
e^2-x
Similar expressions
e^(2+x)

The derivative of the function/ e^(2-x)

Derivative of e^(2-x)

The solution

You have entered [src]

 2 - x
e

$$e^{2 - x}$$

d / 2 - x\
--\e     /
dx

$$\frac{d}{d x} e^{2 - x}$$

Transform

Detail solution

Let $u = 2 - x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 - x\right)$ :
1. Differentiate $2 - x$ term by term:
  1. The derivative of the constant $2$ is zero.
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $-1$
  The result is: $-1$
The result of the chain rule is:

$- e^{2 - x}$

The answer is:

$- e^{2 - x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2 - x
-e

$$- e^{2 - x}$$

Simplify

The second derivative [src]

 2 - x
e

$$e^{2 - x}$$

Simplify

The third derivative [src]

  2 - x
-e

$$- e^{2 - x}$$

Simplify

The graph

Derivative of e^(2-x)