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log(5*x)
The derivative of the function/ log(5*x)

Derivative of log(5*x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(5*x)
log⁡(5x)\log{\left(5 x \right)} 
log(5*x)
Detail solution

  1. Let u=5xu = 5 x.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx5x\frac{d}{d x} 5 x:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: xx goes to 11

      So, the result is: 55

    The result of the chain rule is:

    1x\frac{1}{x}

The answer is:

1x\frac{1}{x}

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
1
-
x
1x\frac{1}{x}
Simplify
The second derivative [src] 
-1 
---
  2
 x
−1x2- \frac{1}{x^{2}}
Simplify
The third derivative [src] 
2 
--
 3
x
2x3\frac{2}{x^{3}}
Simplify
The graph
Derivative of log(5*x)
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