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x^3*log(x)

Derivative of x^3*log(x)

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

from to

Piecewise:

The solution

You have entered [src]
 3       
x *log(x)
x3log(x)x^{3} \log{\left(x \right)}
d / 3       \
--\x *log(x)/
dx           
ddxx3log(x)\frac{d}{d x} x^{3} \log{\left(x \right)}
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)=log(x)g{\left(x \right)} = \log{\left(x \right)}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. The derivative of log(x)\log{\left(x \right)} is 1x\frac{1}{x}.

    The result is: 3x2log(x)+x23 x^{2} \log{\left(x \right)} + x^{2}

  2. Now simplify:

    x2(3log(x)+1)x^{2} \cdot \left(3 \log{\left(x \right)} + 1\right)


The answer is:

x2(3log(x)+1)x^{2} \cdot \left(3 \log{\left(x \right)} + 1\right)

The graph
02468-8-6-4-2-1010-25002500
The first derivative [src]
 2      2       
x  + 3*x *log(x)
3x2log(x)+x23 x^{2} \log{\left(x \right)} + x^{2}
The second derivative [src]
x*(5 + 6*log(x))
x(6log(x)+5)x \left(6 \log{\left(x \right)} + 5\right)
The third derivative [src]
11 + 6*log(x)
6log(x)+116 \log{\left(x \right)} + 11
The graph
Derivative of x^3*log(x)