Mister Exam

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 
8x5\sqrt{8 x - 5}
d /  _________\
--\\/ 8*x - 5 /
dx             
ddx8x5\frac{d}{d x} \sqrt{8 x - 5}
Detail solution
  1. Let u=8x5u = 8 x - 5.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(8x5)\frac{d}{d x} \left(8 x - 5\right):

    1. Differentiate 8x58 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: xx goes to 11

        So, the result is: 88

      2. The derivative of the constant (1)5\left(-1\right) 5 is zero.

      The result is: 88

    The result of the chain rule is:

    48x5\frac{4}{\sqrt{8 x - 5}}

  4. Now simplify:

    48x5\frac{4}{\sqrt{8 x - 5}}


The answer is:

48x5\frac{4}{\sqrt{8 x - 5}}

The graph
02468-8-6-4-2-1010010
The first derivative [src]
     4     
-----------
  _________
\/ 8*x - 5 
48x5\frac{4}{\sqrt{8 x - 5}}
The second derivative [src]
     -16     
-------------
          3/2
(-5 + 8*x)   
16(8x5)32- \frac{16}{\left(8 x - 5\right)^{\frac{3}{2}}}
The third derivative [src]
     192     
-------------
          5/2
(-5 + 8*x)   
192(8x5)52\frac{192}{\left(8 x - 5\right)^{\frac{5}{2}}}
The graph
Derivative of sqrt(8x-5)