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The derivative of the function/ sqrt(8x-5)

Derivative of sqrt(8x-5)

The solution

You have entered [src]

  _________
\/ 8*x - 5

\sqrt{8 x - 5}

d /  _________\
--\\/ 8*x - 5 /
dx

\frac{d}{d x} \sqrt{8 x - 5}

Transform

Detail solution

Let $u = 8 x - 5$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(8 x - 5\right)$ :
1. Differentiate $8 x - 5$ 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: $8$
  2. The derivative of the constant $\left(-1\right) 5$ is zero.
  The result is: $8$
The result of the chain rule is:

$\frac{4}{\sqrt{8 x - 5}}$
Now simplify:

$\frac{4}{\sqrt{8 x - 5}}$

The answer is:

\frac{4}{\sqrt{8 x - 5}}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     4     
-----------
  _________
\/ 8*x - 5

\frac{4}{\sqrt{8 x - 5}}

Simplify

The second derivative [src]

     -16     
-------------
          3/2
(-5 + 8*x)

- \frac{16}{\left(8 x - 5\right)^{\frac{3}{2}}}

Simplify

The third derivative [src]

     192     
-------------
          5/2
(-5 + 8*x)

\frac{192}{\left(8 x - 5\right)^{\frac{5}{2}}}

Simplify

The graph

Derivative of sqrt(8x-5)