Derivative of ln(t)^3

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   3   
log (t)

$$\log{\left(t \right)}^{3}$$

log(t)^3

Detail solution

Let $u = \log{\left(t \right)}$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
Then, apply the chain rule. Multiply by $\frac{d}{d t} \log{\left(t \right)}$ :
1. The derivative of $\log{\left(t \right)}$ is $\frac{1}{t}$ .
The result of the chain rule is:

$\frac{3 \log{\left(t \right)}^{2}}{t}$

The answer is:

$\frac{3 \log{\left(t \right)}^{2}}{t}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2   
3*log (t)
---------
    t

$$\frac{3 \log{\left(t \right)}^{2}}{t}$$

Simplify

The second derivative [src]

3*(2 - log(t))*log(t)
---------------------
           2         
          t

$$\frac{3 \left(2 - \log{\left(t \right)}\right) \log{\left(t \right)}}{t^{2}}$$

Simplify

The third derivative [src]

  /       2              \
6*\1 + log (t) - 3*log(t)/
--------------------------
             3            
            t

$$\frac{6 \left(\log{\left(t \right)}^{2} - 3 \log{\left(t \right)} + 1\right)}{t^{3}}$$

Simplify