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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:

from to

Piecewise:

The solution

You have entered [src] 
log(x) - 4*cos(x)
$$\log{\left(x \right)} - 4 \cos{\left(x \right)}$$ 
log(x) - 4*cos(x)
Detail solution

  1. Differentiate term by term:

    1. The derivative of is .

    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:

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1           
- + 4*sin(x)
x
$$4 \sin{\left(x \right)} + \frac{1}{x}$$
Simplify
The second derivative [src] 
  1            
- -- + 4*cos(x)
   2           
  x
$$4 \cos{\left(x \right)} - \frac{1}{x^{2}}$$
Simplify
The third derivative [src] 
  /1            \
2*|-- - 2*sin(x)|
  | 3           |
  \x            /
$$2 \left(- 2 \sin{\left(x \right)} + \frac{1}{x^{3}}\right)$$
Simplify
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