Mister Exam

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The derivative of the function/ -sqrt(3x+4)

Derivative of -sqrt(3x+4)

The solution

You have entered [src]

   _________
-\/ 3*x + 4

- \sqrt{3 x + 4}

-sqrt(3*x + 4)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x + 4$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 4\right)$ :
  1. Differentiate $3 x + 4$ 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 the constant $4$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $\frac{3}{2 \sqrt{3 x + 4}}$
So, the result is: $- \frac{3}{2 \sqrt{3 x + 4}}$
Now simplify:

$- \frac{3}{2 \sqrt{3 x + 4}}$

The answer is:

- \frac{3}{2 \sqrt{3 x + 4}}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     -3      
-------------
    _________
2*\/ 3*x + 4

- \frac{3}{2 \sqrt{3 x + 4}}

Simplify

The second derivative [src]

      9       
--------------
           3/2
4*(4 + 3*x)

\frac{9}{4 \left(3 x + 4\right)^{\frac{3}{2}}}

Simplify

The third derivative [src]

     -81      
--------------
           5/2
8*(4 + 3*x)

- \frac{81}{8 \left(3 x + 4\right)^{\frac{5}{2}}}

Simplify