Mister Exam

Derivative of lnx-4*cosx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(x) - 4*cos(x)
log(x)4cos(x)\log{\left(x \right)} - 4 \cos{\left(x \right)}
log(x) - 4*cos(x)
Detail solution
  1. Differentiate log(x)4cos(x)\log{\left(x \right)} - 4 \cos{\left(x \right)} term by term:

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

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

      1. The derivative of cosine is negative sine:

        ddxcos(x)=sin(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

      So, the result is: 4sin(x)4 \sin{\left(x \right)}

    The result is: 4sin(x)+1x4 \sin{\left(x \right)} + \frac{1}{x}


The answer is:

4sin(x)+1x4 \sin{\left(x \right)} + \frac{1}{x}

The graph
02468-8-6-4-2-1010-2525
The first derivative [src]
1           
- + 4*sin(x)
x           
4sin(x)+1x4 \sin{\left(x \right)} + \frac{1}{x}
The second derivative [src]
  1            
- -- + 4*cos(x)
   2           
  x            
4cos(x)1x24 \cos{\left(x \right)} - \frac{1}{x^{2}}
The third derivative [src]
  /1            \
2*|-- - 2*sin(x)|
  | 3           |
  \x            /
2(2sin(x)+1x3)2 \left(- 2 \sin{\left(x \right)} + \frac{1}{x^{3}}\right)