Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^(5*x)
Derivative of x^2+x+1
Derivative of (x^2+1)^2
Derivative of sqrt(2*x)
Identical expressions
(x^ two +2x)e^x
(x squared plus 2x)e to the power of x
(x to the power of two plus 2x)e to the power of x
(x2+2x)ex
x2+2xex
(x²+2x)e^x
(x to the power of 2+2x)e to the power of x
x^2+2xe^x
Similar expressions
(x^2-2x)e^x

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

Derivative of (x^2+2x)e^x

The solution

You have entered [src]

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

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

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

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

Transform

Detail solution

Apply the product rule:

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           x   / 2      \  x
(2 + 2*x)*e  + \x  + 2*x/*e

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

Simplify

The second derivative [src]

                       x
(6 + 4*x + x*(2 + x))*e

$$\left(x \left(x + 2\right) + 4 x + 6\right) e^{x}$$

Simplify

The third derivative [src]

                        x
(12 + 6*x + x*(2 + x))*e

$$\left(x \left(x + 2\right) + 6 x + 12\right) e^{x}$$

Simplify

The graph

Derivative of (x^2+2x)e^x