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Derivative of:
Derivative of x^3/(2*x+4)
Derivative of (x^3-2)*(x^2+1)
Derivative of x^2/(x-4)
Derivative of (x^2+24)/(x+1)
Limit of the function:
log(1+t^2)
Identical expressions
log(one +t^ two)
logarithm of (1 plus t squared )
logarithm of (one plus t to the power of two)
log(1+t2)
log1+t2
log(1+t²)
log(1+t to the power of 2)
log1+t^2
Similar expressions
log(1-t^2)

The derivative of the function/ log(1+t^2)

Derivative of log(1+t^2)

The solution

You have entered [src]

   /     2\
log\1 + t /

$$\log{\left(t^{2} + 1 \right)}$$

log(1 + t^2)

Detail solution

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

$\frac{2 t}{t^{2} + 1}$

The answer is:

$\frac{2 t}{t^{2} + 1}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2*t  
------
     2
1 + t

$$\frac{2 t}{t^{2} + 1}$$

Simplify

The second derivative [src]

  /        2 \
  |     2*t  |
2*|1 - ------|
  |         2|
  \    1 + t /
--------------
         2    
    1 + t

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

Simplify

The third derivative [src]

    /         2 \
    |      4*t  |
4*t*|-3 + ------|
    |          2|
    \     1 + t /
-----------------
            2    
    /     2\     
    \1 + t /

$$\frac{4 t \left(\frac{4 t^{2}}{t^{2} + 1} - 3\right)}{\left(t^{2} + 1\right)^{2}}$$

Simplify

The graph

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Derivative of log(1+t^2)

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The solution