Mister Exam

Derivative of y=(2x+1)⁵

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         5
(2*x + 1) 
$$\left(2 x + 1\right)^{5}$$
d /         5\
--\(2*x + 1) /
dx            
$$\frac{d}{d x} \left(2 x + 1\right)^{5}$$
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
The first derivative [src]
            4
10*(2*x + 1) 
$$10 \left(2 x + 1\right)^{4}$$
The second derivative [src]
            3
80*(1 + 2*x) 
$$80 \left(2 x + 1\right)^{3}$$
The third derivative [src]
             2
480*(1 + 2*x) 
$$480 \left(2 x + 1\right)^{2}$$
The graph
Derivative of y=(2x+1)⁵