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The derivative of the function/ 5lnx-2cosx+11

Derivative of 5lnx-2cosx+11

The solution

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5*log(x) - 2*cos(x) + 11

$$\left(5 \log{\left(x \right)} - 2 \cos{\left(x \right)}\right) + 11$$

5*log(x) - 2*cos(x) + 11

Detail solution

Differentiate $\left(5 \log{\left(x \right)} - 2 \cos{\left(x \right)}\right) + 11$ term by term:
1. Differentiate $5 \log{\left(x \right)} - 2 \cos{\left(x \right)}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    So, the result is: $\frac{5}{x}$
  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:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    So, the result is: $2 \sin{\left(x \right)}$
  The result is: $2 \sin{\left(x \right)} + \frac{5}{x}$
2. The derivative of the constant $11$ is zero.
The result is: $2 \sin{\left(x \right)} + \frac{5}{x}$

The answer is:

$2 \sin{\left(x \right)} + \frac{5}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           5
2*sin(x) + -
           x

$$2 \sin{\left(x \right)} + \frac{5}{x}$$

Simplify

The second derivative [src]

  5            
- -- + 2*cos(x)
   2           
  x

$$2 \cos{\left(x \right)} - \frac{5}{x^{2}}$$

Simplify

The third derivative [src]

  /          5 \
2*|-sin(x) + --|
  |           3|
  \          x /

$$2 \left(- \sin{\left(x \right)} + \frac{5}{x^{3}}\right)$$

Simplify