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x^7*e^x

Derivative of x^7*e^x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 7  x
x *E 
$$e^{x} x^{7}$$
x^7*E^x
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Apply the power rule: goes to

    ; to find :

    1. The derivative of is itself.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
 7  x      6  x
x *e  + 7*x *e 
$$x^{7} e^{x} + 7 x^{6} e^{x}$$
The second derivative [src]
 5 /      2       \  x
x *\42 + x  + 14*x/*e 
$$x^{5} \left(x^{2} + 14 x + 42\right) e^{x}$$
The third derivative [src]
 4 /       3       2        \  x
x *\210 + x  + 21*x  + 126*x/*e 
$$x^{4} \left(x^{3} + 21 x^{2} + 126 x + 210\right) e^{x}$$
The graph
Derivative of x^7*e^x