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x^3*e^x
The derivative of the function/ x^3*e^x

You entered:

x^3*e^x

What you mean?

x^3*e^x
 
x^((3*e)^x)
 
x^((3*e)^x)

Derivative of x^3*e^x

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 3  x
x *e
x3exx^{3} e^{x} 
d / 3  x\
--\x *e /
dx
ddxx3ex\frac{d}{d x} x^{3} e^{x}
Transform
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=x3f{\left(x \right)} = x^{3}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x3x^{3} goes to 3x23 x^{2}

    g(x)=exg{\left(x \right)} = e^{x}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of exe^{x} is itself.

    The result is: x3ex+3x2exx^{3} e^{x} + 3 x^{2} e^{x}

  2. Now simplify:

    x2(x+3)exx^{2} \left(x + 3\right) e^{x}

The answer is:

x2(x+3)exx^{2} \left(x + 3\right) e^{x}

The graph
02468-8-6-4-2-1010-5000000050000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 3  x      2  x
x *e  + 3*x *e
x3ex+3x2exx^{3} e^{x} + 3 x^{2} e^{x}
Simplify
The second derivative [src] 
  /     2      \  x
x*\6 + x  + 6*x/*e
x(x2+6x+6)exx \left(x^{2} + 6 x + 6\right) e^{x}
Simplify
The third derivative [src] 
/     3      2       \  x
\6 + x  + 9*x  + 18*x/*e
(x3+9x2+18x+6)ex\left(x^{3} + 9 x^{2} + 18 x + 6\right) e^{x}
Simplify
The graph
Derivative of x^3*e^x
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