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Derivative of:
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Identical expressions
cos(two *x)+ one /x
co sinus of e of (2 multiply by x) plus 1 divide by x
co sinus of e of (two multiply by x) plus one divide by x
cos(2x)+1/x
cos2x+1/x
cos(2*x)+1 divide by x
Similar expressions
(cos^2x+1/x+√x+e^x)
cos(2*x)-1/x

The derivative of the function/ cos(2*x)+1/x

Derivative of cos(2*x)+1/x

The solution

You have entered [src]

           1
cos(2*x) + -
           x

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

cos(2*x) + 1/x

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1              
- -- - 2*sin(2*x)
   2             
  x

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

Simplify

The second derivative [src]

  /1              \
2*|-- - 2*cos(2*x)|
  | 3             |
  \x              /

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

Simplify

The third derivative [src]

  /  3              \
2*|- -- + 4*sin(2*x)|
  |   4             |
  \  x              /

$$2 \left(4 \sin{\left(2 x \right)} - \frac{3}{x^{4}}\right)$$

Simplify