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sqrt(10*x)
The derivative of the function/ sqrt(10*x)

Derivative of sqrt(10*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  ______
\/ 10*x
$$\sqrt{10 x}$$ 
sqrt(10*x)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

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

      1. Apply the power rule: goes to

      So, the result is:

    The result of the chain rule is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  ____   ___
\/ 10 *\/ x 
------------
    2*x
$$\frac{\sqrt{10} \sqrt{x}}{2 x}$$
Simplify
The second derivative [src] 
   ____ 
-\/ 10  
--------
    3/2 
 4*x
$$- \frac{\sqrt{10}}{4 x^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
    ____
3*\/ 10 
--------
    5/2 
 8*x
$$\frac{3 \sqrt{10}}{8 x^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of sqrt(10*x)
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