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

Derivative of 1/(x+3)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1  
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x + 3
1x+3\frac{1}{x + 3} 
1/(x + 3)
Detail solution

  1. Let u=x+3u = x + 3.

  2. Apply the power rule: 1u\frac{1}{u} goes to −1u2- \frac{1}{u^{2}}

  3. Then, apply the chain rule. Multiply by ddx(x+3)\frac{d}{d x} \left(x + 3\right):

    1. Differentiate x+3x + 3 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant 33 is zero.

      The result is: 11

    The result of the chain rule is:

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

  4. Now simplify:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-250250
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  -1    
--------
       2
(x + 3)
−1(x+3)2- \frac{1}{\left(x + 3\right)^{2}}
Simplify
The second derivative [src] 
   2    
--------
       3
(3 + x)
2(x+3)3\frac{2}{\left(x + 3\right)^{3}}
Simplify
The third derivative [src] 
  -6    
--------
       4
(3 + x)
−6(x+3)4- \frac{6}{\left(x + 3\right)^{4}}
Simplify
The graph
Derivative of 1/(x+3)
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