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sqrt(25-9x^2)
The derivative of the function/ sqrt(25-9x^2)

Derivative of sqrt(25-9x^2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___________
  /         2 
\/  25 - 9*x
$$\sqrt{25 - 9 x^{2}}$$ 
  /   ___________\
d |  /         2 |
--\\/  25 - 9*x  /
dx
$$\frac{d}{d x} \sqrt{25 - 9 x^{2}}$$
Transform
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. 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:

        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] 
     -9*x     
--------------
   ___________
  /         2 
\/  25 - 9*x
$$- \frac{9 x}{\sqrt{25 - 9 x^{2}}}$$
Simplify
The second derivative [src] 
   /          2  \
   |       9*x   |
-9*|1 + ---------|
   |            2|
   \    25 - 9*x /
------------------
     ___________  
    /         2   
  \/  25 - 9*x
$$- \frac{9 \cdot \left(\frac{9 x^{2}}{25 - 9 x^{2}} + 1\right)}{\sqrt{25 - 9 x^{2}}}$$
Simplify
The third derivative [src] 
       /          2  \
       |       9*x   |
-243*x*|1 + ---------|
       |            2|
       \    25 - 9*x /
----------------------
               3/2    
    /        2\       
    \25 - 9*x /
$$- \frac{243 x \left(\frac{9 x^{2}}{25 - 9 x^{2}} + 1\right)}{\left(25 - 9 x^{2}\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(25-9x^2)
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