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x*log(x)
The derivative of the function/ x*log(x)

Derivative of x*log(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x*log(x)
xlog⁡(x)x \log{\left(x \right)} 
d           
--(x*log(x))
dx
ddxxlog⁡(x)\frac{d}{d x} x \log{\left(x \right)}
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)=xf{\left(x \right)} = x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    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: log⁡(x)+1\log{\left(x \right)} + 1

The answer is:

log⁡(x)+1\log{\left(x \right)} + 1

The graph
02468-8-6-4-2-1010-2525
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1 + log(x)
log⁡(x)+1\log{\left(x \right)} + 1
Simplify
The second derivative [src] 
1
-
x
1x\frac{1}{x}
Simplify
The third derivative [src] 
-1 
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  2
 x
−1x2- \frac{1}{x^{2}}
Simplify
The graph
Derivative of x*log(x)
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