Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x*cot(x)
Derivative of x^3-3*x^2
Derivative of (x+3)^4
Derivative of (x-3)^3
Integral of d{x}:
1/(x^2+3)
Equation:
1/(x^2+3)
Graphing y =:
1/(x^2+3)
Identical expressions
one /(x^ two + three)
1 divide by (x squared plus 3)
one divide by (x to the power of two plus three)
1/(x2+3)
1/x2+3
1/(x²+3)
1/(x to the power of 2+3)
1/x^2+3
1 divide by (x^2+3)
Similar expressions
1/(x^2-3)

The derivative of the function/ 1/(x^2+3)

Derivative of 1/(x^2+3)

The solution

You have entered [src]

  1   
------
 2    
x  + 3

$$\frac{1}{x^{2} + 3}$$

1/(x^2 + 3)

Detail solution

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

$- \frac{2 x}{\left(x^{2} + 3\right)^{2}}$
Now simplify:

$- \frac{2 x}{\left(x^{2} + 3\right)^{2}}$

The answer is:

$- \frac{2 x}{\left(x^{2} + 3\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -2*x  
---------
        2
/ 2    \ 
\x  + 3/

$$- \frac{2 x}{\left(x^{2} + 3\right)^{2}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

     /        2 \
     |     2*x  |
24*x*|1 - ------|
     |         2|
     \    3 + x /
-----------------
            3    
    /     2\     
    \3 + x /

$$\frac{24 x \left(- \frac{2 x^{2}}{x^{2} + 3} + 1\right)}{\left(x^{2} + 3\right)^{3}}$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of 1/(x^2+3)

The graph:

Piecewise:

The solution