Mister Exam

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The derivative of the function/ -sqrt(x-3)

Derivative of -sqrt(x-3)

The solution

You have entered [src]

   _______
-\/ x - 3

$$- \sqrt{x - 3}$$

-sqrt(x - 3)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x - 3$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 3\right)$ :
  1. Differentiate $x - 3$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $-3$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $\frac{1}{2 \sqrt{x - 3}}$
So, the result is: $- \frac{1}{2 \sqrt{x - 3}}$
Now simplify:

$- \frac{1}{2 \sqrt{x - 3}}$

The answer is:

$- \frac{1}{2 \sqrt{x - 3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -1     
-----------
    _______
2*\/ x - 3

$$- \frac{1}{2 \sqrt{x - 3}}$$

Simplify

The second derivative [src]

      1      
-------------
          3/2
4*(-3 + x)

$$\frac{1}{4 \left(x - 3\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

     -3      
-------------
          5/2
8*(-3 + x)

$$- \frac{3}{8 \left(x - 3\right)^{\frac{5}{2}}}$$

Simplify