Mister Exam

Other calculators

The derivative of the function/ sqrt(25+25x^2)

Derivative of sqrt(25+25x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ____________
  /          2 
\/  25 + 25*x
$$\sqrt{25 x^{2} + 25}$$ 
sqrt(25 + 25*x^2)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. 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 is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      25*x     
---------------
   ____________
  /          2 
\/  25 + 25*x
$$\frac{25 x}{\sqrt{25 x^{2} + 25}}$$
Simplify
The second derivative [src] 
  /       2  \
  |      x   |
5*|1 - ------|
  |         2|
  \    1 + x /
--------------
    ________  
   /      2   
 \/  1 + x
$$\frac{5 \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)}{\sqrt{x^{2} + 1}}$$
Simplify
The third derivative [src] 
     /        2  \
     |       x   |
15*x*|-1 + ------|
     |          2|
     \     1 + x /
------------------
           3/2    
   /     2\       
   \1 + x /
$$\frac{15 x \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{\frac{3}{2}}}$$
Simplify
    © Mister Exam – Calculator