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Derivative of:
Derivative of sqrt(x^2+1)
Derivative of 1/sin(x)
Derivative of log(x+1)
Derivative of acos(x)
Integral of d{x}:
1/(x-3)^2
Identical expressions
one /(x- three)^ two
1 divide by (x minus 3) squared
one divide by (x minus three) to the power of two
1/(x-3)2
1/x-32
1/(x-3)²
1/(x-3) to the power of 2
1/x-3^2
1 divide by (x-3)^2
Similar expressions
1/(x+3)^2

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

Derivative of 1/(x-3)^2

The solution

You have entered [src]

   1    
--------
       2
(x - 3)

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

1/((x - 3)^2)

Detail solution

Let $u = \left(x - 3\right)^{2}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 3\right)^{2}$ :
1. Let $u = x - 3$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 3\right)$ :
  1. Differentiate $x - 3$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $-3$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $2 x - 6$
The result of the chain rule is:

$- \frac{2 x - 6}{\left(x - 3\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     6 - 2*x     
-----------------
       2        2
(x - 3) *(x - 3)

$$\frac{6 - 2 x}{\left(x - 3\right)^{2} \left(x - 3\right)^{2}}$$

Simplify

The second derivative [src]

    6    
---------
        4
(-3 + x)

$$\frac{6}{\left(x - 3\right)^{4}}$$

Simplify

The third derivative [src]

   -24   
---------
        5
(-3 + x)

$$- \frac{24}{\left(x - 3\right)^{5}}$$

Simplify

The graph

Derivative of 1/(x-3)^2