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Derivative of:
Derivative of f(x)=x^3
Derivative of (-6)/x^4
Derivative of 5/x^3
Derivative of y=√4-x^2
Identical expressions
log(one + two *x, ten)
logarithm of (1 plus 2 multiply by x,10)
logarithm of (one plus two multiply by x, ten)
log(1+2x,10)
log1+2x,10
Similar expressions
log(1-2*x,10)

The derivative of the function/ log(1+2*x,10)

Derivative of log(1+2*x,10)

The solution

You have entered [src]

log(1 + 2*x)
------------
  log(10)

$$\frac{\log{\left(2 x + 1 \right)}}{\log{\left(10 \right)}}$$

log(1 + 2*x)/log(10)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x + 1$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x + 1\right)$ :
  1. Differentiate $2 x + 1$ term by term:
    1. The derivative of the constant $1$ is zero.
    2. 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 is: $2$
  The result of the chain rule is:
  
  $\frac{2}{2 x + 1}$
So, the result is: $\frac{2}{\left(2 x + 1\right) \log{\left(10 \right)}}$

The answer is:

$\frac{2}{\left(2 x + 1\right) \log{\left(10 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2        
-----------------
(1 + 2*x)*log(10)

$$\frac{2}{\left(2 x + 1\right) \log{\left(10 \right)}}$$

Simplify

The second derivative [src]

       -4         
------------------
         2        
(1 + 2*x) *log(10)

$$- \frac{4}{\left(2 x + 1\right)^{2} \log{\left(10 \right)}}$$

Simplify

8-я производная [src]

    -1290240      
------------------
         8        
(1 + 2*x) *log(10)

$$- \frac{1290240}{\left(2 x + 1\right)^{8} \log{\left(10 \right)}}$$

Simplify

The third derivative [src]

        16        
------------------
         3        
(1 + 2*x) *log(10)

$$\frac{16}{\left(2 x + 1\right)^{3} \log{\left(10 \right)}}$$

Simplify