Derivative of log(y^2)

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   / 2\
log\y /

$$\log{\left(y^{2} \right)}$$

log(y^2)

Detail solution

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

$\frac{2}{y}$

The answer is:

$\frac{2}{y}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2
-
y

$$\frac{2}{y}$$

Simplify

The second derivative [src]

-2 
---
  2
 y

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

Simplify

The third derivative [src]

4 
--
 3
y

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

Simplify

The graph