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The derivative of the function/ 10lnx-4sinx-5cosx

Derivative of 10lnx-4sinx-5cosx

The solution

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10*log(x) - 4*sin(x) - 5*cos(x)

$$\left(10 \log{\left(x \right)} - 4 \sin{\left(x \right)}\right) - 5 \cos{\left(x \right)}$$

10*log(x) - 4*sin(x) - 5*cos(x)

Detail solution

Differentiate $\left(10 \log{\left(x \right)} - 4 \sin{\left(x \right)}\right) - 5 \cos{\left(x \right)}$ term by term:
1. Differentiate $10 \log{\left(x \right)} - 4 \sin{\left(x \right)}$ 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: $\frac{10}{x}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    So, the result is: $- 4 \cos{\left(x \right)}$
  The result is: $- 4 \cos{\left(x \right)} + \frac{10}{x}$
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: $5 \sin{\left(x \right)}$
The result is: $5 \sin{\left(x \right)} - 4 \cos{\left(x \right)} + \frac{10}{x}$

The answer is:

$5 \sin{\left(x \right)} - 4 \cos{\left(x \right)} + \frac{10}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                       10
-4*cos(x) + 5*sin(x) + --
                       x

$$5 \sin{\left(x \right)} - 4 \cos{\left(x \right)} + \frac{10}{x}$$

Simplify

The second derivative [src]

  10                      
- -- + 4*sin(x) + 5*cos(x)
   2                      
  x

$$4 \sin{\left(x \right)} + 5 \cos{\left(x \right)} - \frac{10}{x^{2}}$$

Simplify

The third derivative [src]

                       20
-5*sin(x) + 4*cos(x) + --
                        3
                       x

$$- 5 \sin{\left(x \right)} + 4 \cos{\left(x \right)} + \frac{20}{x^{3}}$$

Simplify