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Derivative of:
Derivative of sqrt(r^2-x^2)
Derivative of sinx/(3-2cos(x))
Derivative of y=log((sin^2)(4x))
Derivative of y=xlog2x
Integral of d{x}:
sqrt(r^2-x^2)
Identical expressions
sqrt(r^ two -x^ two)
square root of (r squared minus x squared )
square root of (r to the power of two minus x to the power of two)
√(r^2-x^2)
sqrt(r2-x2)
sqrtr2-x2
sqrt(r²-x²)
sqrt(r to the power of 2-x to the power of 2)
sqrtr^2-x^2
Similar expressions
sqrt(r^2+x^2)

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

Derivative of sqrt(r^2-x^2)

The solution

You have entered [src]

   _________
  /  2    2 
\/  r  - x

$$\sqrt{r^{2} - x^{2}}$$

  /   _________\
d |  /  2    2 |
--\\/  r  - x  /
dx

$$\frac{\partial}{\partial x} \sqrt{r^{2} - x^{2}}$$

Transform

Detail solution

Let $u = r^{2} - x^{2}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} \left(r^{2} - x^{2}\right)$ :
1. Differentiate $r^{2} - x^{2}$ term by term:
  1. The derivative of the constant $r^{2}$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $- 2 x$
  The result is: $- 2 x$
The result of the chain rule is:

$- \frac{x}{\sqrt{r^{2} - x^{2}}}$

The answer is:

$- \frac{x}{\sqrt{r^{2} - x^{2}}}$

The first derivative [src]

    -x      
------------
   _________
  /  2    2 
\/  r  - x

$$- \frac{x}{\sqrt{r^{2} - x^{2}}}$$

Simplify

The second derivative [src]

 /        2  \ 
 |       x   | 
-|1 + -------| 
 |     2    2| 
 \    r  - x / 
---------------
     _________ 
    /  2    2  
  \/  r  - x

$$- \frac{\frac{x^{2}}{r^{2} - x^{2}} + 1}{\sqrt{r^{2} - x^{2}}}$$

Simplify

The third derivative [src]

     /        2  \
     |       x   |
-3*x*|1 + -------|
     |     2    2|
     \    r  - x /
------------------
            3/2   
   / 2    2\      
   \r  - x /

$$- \frac{3 x \left(\frac{x^{2}}{r^{2} - x^{2}} + 1\right)}{\left(r^{2} - x^{2}\right)^{\frac{3}{2}}}$$

Simplify

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Derivative of sqrt(r^2-x^2)

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