Mister Exam

Derivative of sqrt(2x+5)

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
  _________
\/ 2*x + 5 
2x+5\sqrt{2 x + 5}
d /  _________\
--\\/ 2*x + 5 /
dx             
ddx2x+5\frac{d}{d x} \sqrt{2 x + 5}
Detail solution
  1. Let u=2x+5u = 2 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(2x+5)\frac{d}{d x} \left(2 x + 5\right):

    1. Differentiate 2x+52 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: 22

      2. The derivative of the constant 55 is zero.

      The result is: 22

    The result of the chain rule is:

    12x+5\frac{1}{\sqrt{2 x + 5}}

  4. Now simplify:

    12x+5\frac{1}{\sqrt{2 x + 5}}


The answer is:

12x+5\frac{1}{\sqrt{2 x + 5}}

The graph
02468-8-6-4-2-1010010
The first derivative [src]
     1     
-----------
  _________
\/ 2*x + 5 
12x+5\frac{1}{\sqrt{2 x + 5}}
The second derivative [src]
    -1      
------------
         3/2
(5 + 2*x)   
1(2x+5)32- \frac{1}{\left(2 x + 5\right)^{\frac{3}{2}}}
The third derivative [src]
     3      
------------
         5/2
(5 + 2*x)   
3(2x+5)52\frac{3}{\left(2 x + 5\right)^{\frac{5}{2}}}
The graph
Derivative of sqrt(2x+5)