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The derivative of the function/ sqrt(10x)/4

Derivative of sqrt(10x)/4

The solution

You have entered [src]

  ______
\/ 10*x 
--------
   4

$$\frac{\sqrt{10 x}}{4}$$

sqrt(10*x)/4

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 10 x$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 10 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $10$
  The result of the chain rule is:
  
  $\frac{\sqrt{10}}{2 \sqrt{x}}$
So, the result is: $\frac{\sqrt{10}}{8 \sqrt{x}}$

The answer is:

$\frac{\sqrt{10}}{8 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   ____
 \/ 10 
-------
    ___
8*\/ x

$$\frac{\sqrt{10}}{8 \sqrt{x}}$$

Simplify

The second derivative [src]

   ____ 
-\/ 10  
--------
    3/2 
16*x

$$- \frac{\sqrt{10}}{16 x^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

    ____
3*\/ 10 
--------
    5/2 
32*x

$$\frac{3 \sqrt{10}}{32 x^{\frac{5}{2}}}$$

Simplify