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The derivative of the function/ 3x-(sqrt(6x-17))

Derivative of 3x-(sqrt(6x-17))

The solution

You have entered [src]

        __________
3*x - \/ 6*x - 17

$$3 x - \sqrt{6 x - 17}$$

3*x - sqrt(6*x - 17)

Detail solution

Differentiate $3 x - \sqrt{6 x - 17}$ 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: $3$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 6 x - 17$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(6 x - 17\right)$ :
    1. Differentiate $6 x - 17$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $6$
      2. The derivative of the constant $-17$ is zero.
      The result is: $6$
    The result of the chain rule is:
    
    $\frac{3}{\sqrt{6 x - 17}}$
  So, the result is: $- \frac{3}{\sqrt{6 x - 17}}$
The result is: $3 - \frac{3}{\sqrt{6 x - 17}}$
Now simplify:

$3 - \frac{3}{\sqrt{6 x - 17}}$

The answer is:

$3 - \frac{3}{\sqrt{6 x - 17}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         3      
3 - ------------
      __________
    \/ 6*x - 17

$$3 - \frac{3}{\sqrt{6 x - 17}}$$

Simplify

The second derivative [src]

      9       
--------------
           3/2
(-17 + 6*x)

$$\frac{9}{\left(6 x - 17\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

     -81      
--------------
           5/2
(-17 + 6*x)

$$- \frac{81}{\left(6 x - 17\right)^{\frac{5}{2}}}$$

Simplify