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

Derivative of sqrt(3-x)

The solution

You have entered [src]

  _______
\/ 3 - x

$$\sqrt{3 - x}$$

sqrt(3 - x)

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of sqrt(3-x)