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sqrt(1-x)
The derivative of the function/ sqrt(1-x)

Derivative of sqrt(1-x)

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

The graph:

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Piecewise:

The solution

You have entered [src] 
  _______
\/ 1 - x
1−x\sqrt{1 - x} 
sqrt(1 - x)
Detail solution

  1. Let u=1−xu = 1 - x.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(1−x)\frac{d}{d x} \left(1 - x\right):

    1. Differentiate 1−x1 - x term by term:

      1. The derivative of the constant 11 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: xx goes to 11

        So, the result is: −1-1

      The result is: −1-1

    The result of the chain rule is:

    −121−x- \frac{1}{2 \sqrt{1 - x}}

The answer is:

−121−x- \frac{1}{2 \sqrt{1 - x}}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -1     
-----------
    _______
2*\/ 1 - x
−121−x- \frac{1}{2 \sqrt{1 - x}}
Simplify
The second derivative [src] 
    -1      
------------
         3/2
4*(1 - x)
−14(1−x)32- \frac{1}{4 \left(1 - x\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
    -3      
------------
         5/2
8*(1 - x)
−38(1−x)52- \frac{3}{8 \left(1 - x\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(1-x)
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