Mister Exam

Other calculators

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

Derivative of sqrt(8x-5)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

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

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate 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: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

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)
    © Mister Exam – Calculator