Mister Exam

Derivative of y=log5x*e

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(5*x)*e
elog(5x)e \log{\left(5 x \right)}
d             
--(log(5*x)*e)
dx            
ddxelog(5x)\frac{d}{d x} e \log{\left(5 x \right)}
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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}

    So, the result is: ex\frac{e}{x}


The answer is:

ex\frac{e}{x}

The graph
02468-8-6-4-2-1010-5050
The first derivative [src]
e
-
x
ex\frac{e}{x}
The second derivative [src]
-e 
---
  2
 x 
ex2- \frac{e}{x^{2}}
The third derivative [src]
2*e
---
  3
 x 
2ex3\frac{2 e}{x^{3}}
The graph
Derivative of y=log5x*e