Mister Exam

Lang:

The derivative of the function/ y=ln(5x^2)

Derivative of y=ln(5x^2)

The solution

You have entered [src]

   /   2\
log\5*x /

$$\log{\left(5 x^{2} \right)}$$

log(5*x^2)

Detail solution

Let $u = 5 x^{2}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x^{2}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $10 x$
The result of the chain rule is:

$\frac{2}{x}$

The answer is:

$\frac{2}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2
-
x

$$\frac{2}{x}$$

Simplify

The second derivative [src]

-2 
---
  2
 x

$$- \frac{2}{x^{2}}$$

Simplify

The third derivative [src]

4 
--
 3
x

$$\frac{4}{x^{3}}$$

Simplify

The graph

Derivative of y=ln(5x^2)