Mister Exam

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

Derivative of xe^2(-x)

The solution

You have entered [src]

   2   
x*e *-x

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

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

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the product rule:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
    1. Apply the power rule: $x$ goes to $1$
    $g{\left(x \right)} = x$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
    1. Apply the power rule: $x$ goes to $1$
    The result is: $2 x$
  So, the result is: $- 2 x$
So, the result is: $- 2 x e^{2}$

The answer is:

$- 2 x e^{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2
-2*x*e

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

Simplify

The second derivative [src]

    2
-2*e

$$- 2 e^{2}$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of xe^2(-x)