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

Derivative of y=x√a²-x²

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

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The solution

You have entered [src] 
       2     
    ___     2
x*\/ a   - x
x(a)2−x2x \left(\sqrt{a}\right)^{2} - x^{2} 
  /       2     \
d |    ___     2|
--\x*\/ a   - x /
dx
∂∂x(x(a)2−x2)\frac{\partial}{\partial x} \left(x \left(\sqrt{a}\right)^{2} - x^{2}\right)
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Detail solution

  1. Differentiate x(a)2−x2x \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: xx goes to 11

      So, the result is: (a)2\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: x2x^{2} goes to 2x2 x

      So, the result is: −2x- 2 x

    The result is: (a)2−2x\left(\sqrt{a}\right)^{2} - 2 x

  2. Now simplify:

    a−2xa - 2 x

The answer is:

a−2xa - 2 x

The first derivative [src] 
     2      
  ___       
\/ a   - 2*x
(a)2−2x\left(\sqrt{a}\right)^{2} - 2 x
Simplify
The second derivative [src] 
-2
−2-2
Simplify
The third derivative [src] 
0
00
Simplify
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