Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of ln(1-x)
Derivative of ln(x+2)
Derivative of sin(x/3)^(2)*cot(x/2)
Derivative of sin(x)-x*cos(x)
Identical expressions
e^(two *x)+log2x
e to the power of (2 multiply by x) plus logarithm of 2x
e to the power of (two multiply by x) plus logarithm of 2x
e(2*x)+log2x
e2*x+log2x
e^(2x)+log2x
e(2x)+log2x
e2x+log2x
e^2x+log2x
Similar expressions
e^(2*x)-log2x

The derivative of the function/ e^(2*x)+log2x

Derivative of e^(2*x)+log2x

The solution

You have entered [src]

 2*x           
e    + log(2*x)

$$e^{2 x} + \log{\left(2 x \right)}$$

d / 2*x           \
--\e    + log(2*x)/
dx

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

Transform

Detail solution

Differentiate $e^{2 x} + \log{\left(2 x \right)}$ 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. Let $u = 2 x$ .
5. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
6. 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:
  
  $\frac{1}{x}$
The result is: $2 e^{2 x} + \frac{1}{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1      2*x
- + 2*e   
x

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

Simplify

The second derivative [src]

  1       2*x
- -- + 4*e   
   2         
  x

$$4 e^{2 x} - \frac{1}{x^{2}}$$

Simplify

The third derivative [src]

  /1       2*x\
2*|-- + 4*e   |
  | 3         |
  \x          /

$$2 \cdot \left(4 e^{2 x} + \frac{1}{x^{3}}\right)$$

Simplify

The graph

Derivative of e^(2*x)+log2x