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x^7*e^x

Derivative of x^7*e^x

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

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Piecewise:

The solution

You have entered [src]
 7  x
x *E 
exx7e^{x} x^{7}
x^7*E^x
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)=x7f{\left(x \right)} = x^{7}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x7x^{7} goes to 7x67 x^{6}

    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: x7ex+7x6exx^{7} e^{x} + 7 x^{6} e^{x}

  2. Now simplify:

    x6(x+7)exx^{6} \left(x + 7\right) e^{x}


The answer is:

x6(x+7)exx^{6} \left(x + 7\right) e^{x}

The graph
02468-8-6-4-2-1010-500000000000500000000000
The first derivative [src]
 7  x      6  x
x *e  + 7*x *e 
x7ex+7x6exx^{7} e^{x} + 7 x^{6} e^{x}
The second derivative [src]
 5 /      2       \  x
x *\42 + x  + 14*x/*e 
x5(x2+14x+42)exx^{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 
x4(x3+21x2+126x+210)exx^{4} \left(x^{3} + 21 x^{2} + 126 x + 210\right) e^{x}
The graph
Derivative of x^7*e^x