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The derivative of the function/ y=x√a²-x²

Derivative of y=x√a²-x²

The solution

You have entered [src]

       2     
    ___     2
x*\/ a   - x

$$x \left(\sqrt{a}\right)^{2} - x^{2}$$

  /       2     \
d |    ___     2|
--\x*\/ a   - x /
dx

$$\frac{\partial}{\partial x} \left(x \left(\sqrt{a}\right)^{2} - x^{2}\right)$$

Transform

Detail solution

Differentiate $x \left(\sqrt{a}\right)^{2} - x^{2}$ term by term:
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: $\left(\sqrt{a}\right)^{2}$
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: $\left(\sqrt{a}\right)^{2} - 2 x$
Now simplify:

$a - 2 x$

The answer is:

$a - 2 x$

The first derivative [src]

     2      
  ___       
\/ a   - 2*x

$$\left(\sqrt{a}\right)^{2} - 2 x$$

Simplify

The second derivative [src]

-2

$$-2$$

Simplify

The third derivative [src]

$$0$$

Simplify