Mister Exam

Derivative of ln(ax)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(a*x)
log(ax)\log{\left(a x \right)}
log(a*x)
Detail solution
  1. Let u=axu = a x.

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

  3. Then, apply the chain rule. Multiply by xax\frac{\partial}{\partial x} a 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: aa

    The result of the chain rule is:

    1x\frac{1}{x}


The answer is:

1x\frac{1}{x}

The first derivative [src]
1
-
x
1x\frac{1}{x}
The second derivative [src]
-1 
---
  2
 x 
1x2- \frac{1}{x^{2}}
The third derivative [src]
2 
--
 3
x 
2x3\frac{2}{x^{3}}