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Derivative of:
Derivative of tanh(x)
Derivative of cos²x
Derivative of 2*x/(x-2)
Derivative of (π-2x)³
Identical expressions
sqrt(four + eight *x)
square root of (4 plus 8 multiply by x)
square root of (four plus eight multiply by x)
√(4+8*x)
sqrt(4+8x)
sqrt4+8x
Similar expressions
sqrt(4-8*x)

The derivative of the function/ sqrt(4+8*x)

Derivative of sqrt(4+8*x)

The solution

You have entered [src]

  _________
\/ 4 + 8*x

$$\sqrt{8 x + 4}$$

sqrt(4 + 8*x)

Detail solution

Let $u = 8 x + 4$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(8 x + 4\right)$ :
1. Differentiate $8 x + 4$ term by term:
  1. The derivative of the constant $4$ 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: $8$
  The result is: $8$
The result of the chain rule is:

$\frac{4}{\sqrt{8 x + 4}}$
Now simplify:

$\frac{2}{\sqrt{2 x + 1}}$

The answer is:

$\frac{2}{\sqrt{2 x + 1}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     4     
-----------
  _________
\/ 4 + 8*x

$$\frac{4}{\sqrt{8 x + 4}}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

     6      
------------
         5/2
(1 + 2*x)

$$\frac{6}{\left(2 x + 1\right)^{\frac{5}{2}}}$$

Simplify