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Derivative of:
Derivative of e^cos(x)
Derivative of ln(x+3)^3
Derivative of cos(3*x)^(2)
Derivative of -cos(2*x)
Integral of d{x}:
x^6*e^x
Graphing y =:
x^6*e^x
Identical expressions
x^ six *e^x
x to the power of 6 multiply by e to the power of x
x to the power of six multiply by e to the power of x
x6*ex
x⁶*e^x
x^6e^x
x6ex

The derivative of the function/ x^6*e^x

Derivative of x^6*e^x

The solution

You have entered [src]

 6  x
x *E

$$e^{x} x^{6}$$

x^6*E^x

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = x^{6}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
$g{\left(x \right)} = e^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. The derivative of $e^{x}$ is itself.
The result is: $x^{6} e^{x} + 6 x^{5} e^{x}$
Now simplify:

$x^{5} \left(x + 6\right) e^{x}$

The answer is:

$x^{5} \left(x + 6\right) e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 6  x      5  x
x *e  + 6*x *e

$$x^{6} e^{x} + 6 x^{5} e^{x}$$

Simplify

The second derivative [src]

 4 /      2       \  x
x *\30 + x  + 12*x/*e

$$x^{4} \left(x^{2} + 12 x + 30\right) e^{x}$$

Simplify

The third derivative [src]

 3 /       3       2       \  x
x *\120 + x  + 18*x  + 90*x/*e

$$x^{3} \left(x^{3} + 18 x^{2} + 90 x + 120\right) e^{x}$$

Simplify

The graph

Derivative of x^6*e^x