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Derivative of:
Derivative of 2*x^5
Derivative of 5-7x
Derivative of e^x*x^2
Derivative of 2*sqrt(x^3)
Integral of d{x}:
e^x*x^2
Graphing y =:
e^x*x^2
Limit of the function:
e^x*x^2
Identical expressions
e^x*x^ two
e to the power of x multiply by x squared
e to the power of x multiply by x to the power of two
ex*x2
e^x*x²
e to the power of x*x to the power of 2
e^xx^2
exx2

The derivative of the function/ e^x*x^2

Derivative of e^x*x^2

The solution

You have entered [src]

 x  2
E *x

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

E^x*x^2

Detail solution

Apply the product rule:

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

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

The third derivative [src]

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

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

Simplify

The graph

Derivative of e^x*x^2