Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of sin(x)+cos(x)
Derivative of cos(x)^2
Derivative of sin(x^3)
Derivative of log(x)^2
Graphing y =:
x-2+sin(1/x)
Identical expressions
x- two +sin(one /x)
x minus 2 plus sinus of (1 divide by x)
x minus two plus sinus of (one divide by x)
x-2+sin1/x
x-2+sin(1 divide by x)
Similar expressions
x+2+sin(1/x)
x-2-sin(1/x)

The derivative of the function/ x-2+sin(1/x)

Derivative of x-2+sin(1/x)

The solution

You have entered [src]

           /1\
x - 2 + sin|-|
           \x/

$$\left(x - 2\right) + \sin{\left(\frac{1}{x} \right)}$$

x - 2 + sin(1/x)

Detail solution

Differentiate $\left(x - 2\right) + \sin{\left(\frac{1}{x} \right)}$ term by term:
1. Differentiate $x - 2$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $-2$ is zero.
  The result is: $1$
2. Let $u = \frac{1}{x}$ .
3. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{x}$ :
  1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
  The result of the chain rule is:
  
  $- \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}$
The result is: $1 - \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}$

The answer is:

$1 - \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       /1\
    cos|-|
       \x/
1 - ------
       2  
      x

$$1 - \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}$$

Simplify

The second derivative [src]

              /1\
           sin|-|
     /1\      \x/
2*cos|-| - ------
     \x/     x   
-----------------
         3       
        x

$$\frac{2 \cos{\left(\frac{1}{x} \right)} - \frac{\sin{\left(\frac{1}{x} \right)}}{x}}{x^{3}}$$

Simplify

The third derivative [src]

                /1\        /1\
             cos|-|   6*sin|-|
       /1\      \x/        \x/
- 6*cos|-| + ------ + --------
       \x/      2        x    
               x              
------------------------------
               4              
              x

$$\frac{- 6 \cos{\left(\frac{1}{x} \right)} + \frac{6 \sin{\left(\frac{1}{x} \right)}}{x} + \frac{\cos{\left(\frac{1}{x} \right)}}{x^{2}}}{x^{4}}$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of x-2+sin(1/x)

The graph:

Piecewise:

The solution