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The derivative of the function/ lnx-4*cosx

Derivative of lnx-4*cosx

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

The graph:

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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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1           
- + 4*sin(x)
x
4sin⁡(x)+1x4 \sin{\left(x \right)} + \frac{1}{x}
Simplify
The second derivative [src] 
  1            
- -- + 4*cos(x)
   2           
  x
4cos⁡(x)−1x24 \cos{\left(x \right)} - \frac{1}{x^{2}}
Simplify
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)
Simplify
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