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The derivative of the function/ sqrt(7-4x)

Derivative of sqrt(7-4x)

The solution

You have entered [src]

  _________
\/ 7 - 4*x

$$\sqrt{7 - 4 x}$$

sqrt(7 - 4*x)

Detail solution

Let $u = 7 - 4 x$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(7 - 4 x\right)$ :
1. Differentiate $7 - 4 x$ term by term:
  1. The derivative of the constant $7$ 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: $-4$
  The result is: $-4$
The result of the chain rule is:

$- \frac{2}{\sqrt{7 - 4 x}}$

The answer is:

$- \frac{2}{\sqrt{7 - 4 x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -2     
-----------
  _________
\/ 7 - 4*x

$$- \frac{2}{\sqrt{7 - 4 x}}$$

Simplify

The second derivative [src]

    -4      
------------
         3/2
(7 - 4*x)

$$- \frac{4}{\left(7 - 4 x\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

    -24     
------------
         5/2
(7 - 4*x)

$$- \frac{24}{\left(7 - 4 x\right)^{\frac{5}{2}}}$$

Simplify