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(x+3)^2*(x+5)-1

Derivative of (x+3)^2*(x+5)-1

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
       2            
(x + 3) *(x + 5) - 1
$$\left(x + 3\right)^{2} \left(x + 5\right) - 1$$
(x + 3)^2*(x + 5) - 1
Detail solution
  1. Differentiate term by term:

    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. Apply the power rule: goes to

          2. The derivative of the constant is zero.

          The result is:

        The result of the chain rule is:

      ; to find :

      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 is:

    2. The derivative of the constant is zero.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       2                    
(x + 3)  + (6 + 2*x)*(x + 5)
$$\left(x + 3\right)^{2} + \left(x + 5\right) \left(2 x + 6\right)$$
The second derivative [src]
2*(11 + 3*x)
$$2 \left(3 x + 11\right)$$
The third derivative [src]
6
$$6$$
The graph
Derivative of (x+3)^2*(x+5)-1