Mister Exam

Derivative of x^4lnx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 4       
x *log(x)
x4log(x)x^{4} \log{\left(x \right)}
d / 4       \
--\x *log(x)/
dx           
ddxx4log(x)\frac{d}{d x} x^{4} \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)=x4f{\left(x \right)} = x^{4}; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

    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: 4x3log(x)+x34 x^{3} \log{\left(x \right)} + x^{3}

  2. Now simplify:

    x3(4log(x)+1)x^{3} \cdot \left(4 \log{\left(x \right)} + 1\right)


The answer is:

x3(4log(x)+1)x^{3} \cdot \left(4 \log{\left(x \right)} + 1\right)

The graph
02468-8-6-4-2-1010-2500025000
The first derivative [src]
 3      3       
x  + 4*x *log(x)
4x3log(x)+x34 x^{3} \log{\left(x \right)} + x^{3}
The second derivative [src]
 2                
x *(7 + 12*log(x))
x2(12log(x)+7)x^{2} \cdot \left(12 \log{\left(x \right)} + 7\right)
The third derivative [src]
2*x*(13 + 12*log(x))
2x(12log(x)+13)2 x \left(12 \log{\left(x \right)} + 13\right)
The graph
Derivative of x^4lnx