Mister Exam

Derivative of 3xlogx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*x*log(x)
3xlog(x)3 x \log{\left(x \right)}
(3*x)*log(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)=3xf{\left(x \right)} = 3 x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: xx goes to 11

      So, the result is: 33

    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: 3log(x)+33 \log{\left(x \right)} + 3


The answer is:

3log(x)+33 \log{\left(x \right)} + 3

The graph
02468-8-6-4-2-1010-100100
The first derivative [src]
3 + 3*log(x)
3log(x)+33 \log{\left(x \right)} + 3
The second derivative [src]
3
-
x
3x\frac{3}{x}
The third derivative [src]
-3 
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  2
 x 
3x2- \frac{3}{x^{2}}
The graph
Derivative of 3xlogx