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Derivative of:
Derivative of x^-(4/5)
Derivative of ln(x^2-2x)
Derivative of 2*x-x^2
Derivative of 2^x*x^2
Graphing y =:
(x^2)*exp(x)
Identical expressions
(x^ two)*exp(x)
(x squared ) multiply by exponent of (x)
(x to the power of two) multiply by exponent of (x)
(x2)*exp(x)
x2*expx
(x²)*exp(x)
(x to the power of 2)*exp(x)
(x^2)exp(x)
(x2)exp(x)
x2expx
x^2expx

The derivative of the function/ (x^2)*exp(x)

Derivative of (x^2)*exp(x)

The solution

You have entered [src]

 2  x
x *e

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

x^2*exp(x)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $x^{2} e^{x} + 2 x e^{x}$
Now simplify:

$x \left(x + 2\right) e^{x}$

The answer is:

$x \left(x + 2\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2  x        x
x *e  + 2*x*e

$$x^{2} e^{x} + 2 x e^{x}$$

Simplify

The second derivative [src]

/     2      \  x
\2 + x  + 4*x/*e

$$\left(x^{2} + 4 x + 2\right) e^{x}$$

Simplify

5-я производная [src]

/      2       \  x
\20 + x  + 10*x/*e

$$\left(x^{2} + 10 x + 20\right) e^{x}$$

Simplify

The third derivative [src]

/     2      \  x
\6 + x  + 6*x/*e

$$\left(x^{2} + 6 x + 6\right) e^{x}$$

Simplify