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

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

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
/ 3    \  x
\x  - 3/*e
(x3−3)ex\left(x^{3} - 3\right) e^{x} 
d // 3    \  x\
--\\x  - 3/*e /
dx
ddx(x3−3)ex\frac{d}{d x} \left(x^{3} - 3\right) 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)=x3−3f{\left(x \right)} = x^{3} - 3; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate x3−3x^{3} - 3 term by term:

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

      2. The derivative of the constant (−1)3\left(-1\right) 3 is zero.

      The result is: 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: 3x2ex+(x3−3)ex3 x^{2} e^{x} + \left(x^{3} - 3\right) e^{x}

  2. Now simplify:

    (x3+3x2−3)ex\left(x^{3} + 3 x^{2} - 3\right) e^{x}

The answer is:

(x3+3x2−3)ex\left(x^{3} + 3 x^{2} - 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  - 3/*e  + 3*x *e
3x2ex+(x3−3)ex3 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
(x3+6x2+6x−3)ex\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
(x3+9x2+18x+3)ex\left(x^{3} + 9 x^{2} + 18 x + 3\right) e^{x}
Simplify
The graph
Derivative of (x^3-3)*e^x
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