Mister Exam

Lang:

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

Derivative of 4/sqrt(x)

The solution

You have entered [src]

  4  
-----
  ___
\/ x

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

4/sqrt(x)

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2  
----
 3/2
x

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

Simplify

The second derivative [src]

 3  
----
 5/2
x

$$\frac{3}{x^{\frac{5}{2}}}$$

Simplify

The third derivative [src]

 -15  
------
   7/2
2*x

$$- \frac{15}{2 x^{\frac{7}{2}}}$$

Simplify

The graph

Derivative of 4/sqrt(x)