Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^(5*x)
Derivative of x^2+x+1
Derivative of x^2*e^(-x)
Derivative of x^3*tan(x)
Integral of d{x}:
1/(x^2+25)
How do you in partial fractions?:
1/(x^2+25)
Graphing y =:
1/(x^2+25)
Identical expressions
one /(x^ two + twenty-five)
1 divide by (x squared plus 25)
one divide by (x to the power of two plus twenty minus five)
1/(x2+25)
1/x2+25
1/(x²+25)
1/(x to the power of 2+25)
1/x^2+25
1 divide by (x^2+25)
Similar expressions
1/(x^2-25)

The derivative of the function/ 1/(x^2+25)

Derivative of 1/(x^2+25)

The solution

You have entered [src]

     1   
1*-------
   2     
  x  + 25

$$1 \cdot \frac{1}{x^{2} + 25}$$

d /     1   \
--|1*-------|
dx|   2     |
  \  x  + 25/

$$\frac{d}{d x} 1 \cdot \frac{1}{x^{2} + 25}$$

Transform

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = 1$ and $g{\left(x \right)} = x^{2} + 25$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. The derivative of the constant $1$ is zero.
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x^{2} + 25$ term by term:
  1. The derivative of the constant $25$ is zero.
  2. Apply the power rule: $x^{2}$ goes to $2 x$
  The result is: $2 x$
Now plug in to the quotient rule:

$- \frac{2 x}{\left(x^{2} + 25\right)^{2}}$

The answer is:

$- \frac{2 x}{\left(x^{2} + 25\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -2*x   
----------
         2
/ 2     \ 
\x  + 25/

$$- \frac{2 x}{\left(x^{2} + 25\right)^{2}}$$

Simplify

The second derivative [src]

  /          2 \
  |       4*x  |
2*|-1 + -------|
  |           2|
  \     25 + x /
----------------
            2   
   /      2\    
   \25 + x /

$$\frac{2 \cdot \left(\frac{4 x^{2}}{x^{2} + 25} - 1\right)}{\left(x^{2} + 25\right)^{2}}$$

Simplify

The third derivative [src]

      /          2 \
      |       2*x  |
-24*x*|-1 + -------|
      |           2|
      \     25 + x /
--------------------
              3     
     /      2\      
     \25 + x /

$$- \frac{24 x \left(\frac{2 x^{2}}{x^{2} + 25} - 1\right)}{\left(x^{2} + 25\right)^{3}}$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of 1/(x^2+25)

The graph:

Piecewise:

The solution