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The derivative of the function/ 6sqrt(5x+1)

Derivative of 6sqrt(5x+1)

The solution

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    _________
6*\/ 5*x + 1

$$6 \sqrt{5 x + 1}$$

6*sqrt(5*x + 1)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 5 x + 1$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(5 x + 1\right)$ :
  1. Differentiate $5 x + 1$ 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: $5$
    2. The derivative of the constant $1$ is zero.
    The result is: $5$
  The result of the chain rule is:
  
  $\frac{5}{2 \sqrt{5 x + 1}}$
So, the result is: $\frac{15}{\sqrt{5 x + 1}}$
Now simplify:

$\frac{15}{\sqrt{5 x + 1}}$

The answer is:

$\frac{15}{\sqrt{5 x + 1}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     15    
-----------
  _________
\/ 5*x + 1

$$\frac{15}{\sqrt{5 x + 1}}$$

Simplify

The second derivative [src]

     -75      
--------------
           3/2
2*(1 + 5*x)

$$- \frac{75}{2 \left(5 x + 1\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

     1125     
--------------
           5/2
4*(1 + 5*x)

$$\frac{1125}{4 \left(5 x + 1\right)^{\frac{5}{2}}}$$

Simplify