Mister Exam

Derivative of y=(2x-1)³(x+2)²

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
         3        2
(2*x - 1) *(x + 2) 
$$\left(x + 2\right)^{2} \left(2 x - 1\right)^{3}$$
d /         3        2\
--\(2*x - 1) *(x + 2) /
dx                     
$$\frac{d}{d x} \left(x + 2\right)^{2} \left(2 x - 1\right)^{3}$$
Detail solution
  1. Apply the product rule:

    ; to find :

    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:

    ; to find :

    1. Let .

    2. Apply the power rule: goes to

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

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
         3                      2          2
(2*x - 1) *(4 + 2*x) + 6*(x + 2) *(2*x - 1) 
$$6 \left(x + 2\right)^{2} \left(2 x - 1\right)^{2} + \left(2 x + 4\right) \left(2 x - 1\right)^{3}$$
The second derivative [src]
             /          2             2                        \
2*(-1 + 2*x)*\(-1 + 2*x)  + 12*(2 + x)  + 12*(-1 + 2*x)*(2 + x)/
$$2 \cdot \left(2 x - 1\right) \left(12 \left(x + 2\right)^{2} + 12 \left(x + 2\right) \left(2 x - 1\right) + \left(2 x - 1\right)^{2}\right)$$
The third derivative [src]
   /            2            2                        \
12*\3*(-1 + 2*x)  + 4*(2 + x)  + 12*(-1 + 2*x)*(2 + x)/
$$12 \cdot \left(4 \left(x + 2\right)^{2} + 12 \left(x + 2\right) \left(2 x - 1\right) + 3 \left(2 x - 1\right)^{2}\right)$$
The graph
Derivative of y=(2x-1)³(x+2)²