Mister Exam

Derivative of y=(2x+3)⁴

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         4
(2*x + 3) 
$$\left(2 x + 3\right)^{4}$$
d /         4\
--\(2*x + 3) /
dx            
$$\frac{d}{d x} \left(2 x + 3\right)^{4}$$
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]
           3
8*(2*x + 3) 
$$8 \left(2 x + 3\right)^{3}$$
The second derivative [src]
            2
48*(3 + 2*x) 
$$48 \left(2 x + 3\right)^{2}$$
The third derivative [src]
192*(3 + 2*x)
$$192 \cdot \left(2 x + 3\right)$$
The graph
Derivative of y=(2x+3)⁴