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Derivative of:
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Derivative of ln1
Equation:
e^(2*x)+1/x
Identical expressions
e^(two *x)+ one /x
e to the power of (2 multiply by x) plus 1 divide by x
e to the power of (two multiply by x) plus one divide by x
e(2*x)+1/x
e2*x+1/x
e^(2x)+1/x
e(2x)+1/x
e2x+1/x
e^2x+1/x
e^(2*x)+1 divide by x
Similar expressions
e^(2*x)-1/x
What you mean?
(e^(2*x) + 1)/x
e*(2*x + 1)/x
e^(2*x + 1)/x
e^(2*x) + 1/x
e^(2*x) + 1/x

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

You entered:

e^(2*x)+1/x

What you mean?

(e^(2*x) + 1)/x

e*(2*x + 1)/x

e^(2*x + 1)/x

e^(2*x) + 1/x

e^(2*x) + 1/x

Derivative of e^(2*x)+1/x

The solution

You have entered [src]

 2*x     1
e    + 1*-
         x

$$e^{2 x} + 1 \cdot \frac{1}{x}$$

d / 2*x     1\
--|e    + 1*-|
dx\         x/

$$\frac{d}{d x} \left(e^{2 x} + 1 \cdot \frac{1}{x}\right)$$

Transform

Detail solution

Differentiate $e^{2 x} + 1 \cdot \frac{1}{x}$ term by term:
1. Let $u = 2 x$ .
2. The derivative of $e^{u}$ is itself.
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:
  
  $2 e^{2 x}$
4. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = 1$ and $g{\left(x \right)} = x$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. The derivative of the constant $1$ is zero.
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  Now plug in to the quotient rule:
  
  $- \frac{1}{x^{2}}$
The result is: $2 e^{2 x} - \frac{1}{x^{2}}$

The answer is:

$2 e^{2 x} - \frac{1}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1       2*x
- -- + 2*e   
   2         
  x

$$2 e^{2 x} - \frac{1}{x^{2}}$$

Simplify

The second derivative [src]

  /1       2*x\
2*|-- + 2*e   |
  | 3         |
  \x          /

$$2 \cdot \left(2 e^{2 x} + \frac{1}{x^{3}}\right)$$

Simplify

The third derivative [src]

  /  3       2*x\
2*|- -- + 4*e   |
  |   4         |
  \  x          /

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

Simplify

The graph

Derivative of e^(2*x)+1/x