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4/sqrt(x)
The derivative of the function/ 4/sqrt(x)

Derivative of 4/sqrt(x)

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
  4  
-----
  ___
\/ x
4x\frac{4}{\sqrt{x}} 
4/sqrt(x)
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=xu = \sqrt{x}.

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

    3. Then, apply the chain rule. Multiply by ddxx\frac{d}{d x} \sqrt{x}:

      1. Apply the power rule: x\sqrt{x} goes to 12x\frac{1}{2 \sqrt{x}}

      The result of the chain rule is:

      −12x32- \frac{1}{2 x^{\frac{3}{2}}}

    So, the result is: −2x32- \frac{2}{x^{\frac{3}{2}}}

The answer is:

−2x32- \frac{2}{x^{\frac{3}{2}}}

The graph
02468-8-6-4-2-1010-100100
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-2  
----
 3/2
x
−2x32- \frac{2}{x^{\frac{3}{2}}}
Simplify
The second derivative [src] 
 3  
----
 5/2
x
3x52\frac{3}{x^{\frac{5}{2}}}
Simplify
The third derivative [src] 
 -15  
------
   7/2
2*x
−152x72- \frac{15}{2 x^{\frac{7}{2}}}
Simplify
The graph
Derivative of 4/sqrt(x)
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