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5/x^2

Derivative of 5/x^2

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

The graph:

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The solution

You have entered [src]
5 
--
 2
x 
5x2\frac{5}{x^{2}}
5/x^2
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=x2u = x^{2}.

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

    3. Then, apply the chain rule. Multiply by ddxx2\frac{d}{d x} x^{2}:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      The result of the chain rule is:

      2x3- \frac{2}{x^{3}}

    So, the result is: 10x3- \frac{10}{x^{3}}


The answer is:

10x3- \frac{10}{x^{3}}

The graph
02468-8-6-4-2-1010-2000020000
The first derivative [src]
-10 
----
  3 
 x  
10x3- \frac{10}{x^{3}}
The second derivative [src]
30
--
 4
x 
30x4\frac{30}{x^{4}}
The third derivative [src]
-120 
-----
   5 
  x  
120x5- \frac{120}{x^{5}}
The graph
Derivative of 5/x^2