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Derivative of:
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Identical expressions
(x^ three - three)*e^x
(x cubed minus 3) multiply by e to the power of x
(x to the power of three minus three) multiply by e to the power of x
(x3-3)*ex
x3-3*ex
(x³-3)*e^x
(x to the power of 3-3)*e to the power of x
(x^3-3)e^x
(x3-3)ex
x3-3ex
x^3-3e^x
Similar expressions
(x^3+3)*e^x

The derivative of the function/ (x^3-3)*e^x

Derivative of (x^3-3)*e^x

The solution

You have entered [src]

/ 3    \  x
\x  - 3/*e

$$\left(x^{3} - 3\right) e^{x}$$

d // 3    \  x\
--\\x  - 3/*e /
dx

$$\frac{d}{d x} \left(x^{3} - 3\right) e^{x}$$

Transform

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{3} - 3$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x^{3} - 3$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. The derivative of the constant $\left(-1\right) 3$ is zero.
  The result is: $3 x^{2}$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $3 x^{2} e^{x} + \left(x^{3} - 3\right) e^{x}$
Now simplify:

$\left(x^{3} + 3 x^{2} - 3\right) e^{x}$

The answer is:

$\left(x^{3} + 3 x^{2} - 3\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

/ 3    \  x      2  x
\x  - 3/*e  + 3*x *e

$$3 x^{2} e^{x} + \left(x^{3} - 3\right) e^{x}$$

Simplify

The second derivative [src]

/      3            2\  x
\-3 + x  + 6*x + 6*x /*e

$$\left(x^{3} + 6 x^{2} + 6 x - 3\right) e^{x}$$

Simplify

The third derivative [src]

/     3      2       \  x
\3 + x  + 9*x  + 18*x/*e

$$\left(x^{3} + 9 x^{2} + 18 x + 3\right) e^{x}$$

Simplify

The graph

Derivative of (x^3-3)*e^x