Mister Exam

Derivative of (5x-9x³)(8+x²)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
/         3\ /     2\
\5*x - 9*x /*\8 + x /
$$\left(x^{2} + 8\right) \left(- 9 x^{3} + 5 x\right)$$
d //         3\ /     2\\
--\\5*x - 9*x /*\8 + x //
dx                       
$$\frac{d}{d x} \left(x^{2} + 8\right) \left(- 9 x^{3} + 5 x\right)$$
Detail solution
  1. Apply the product rule:

    ; to find :

    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 a constant times a function is the constant times the derivative of the function.

        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:

        So, the result is:

      The result is:

    ; to find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
/        2\ /     2\       /         3\
\5 - 27*x /*\8 + x / + 2*x*\5*x - 9*x /
$$2 x \left(- 9 x^{3} + 5 x\right) + \left(5 - 27 x^{2}\right) \left(x^{2} + 8\right)$$
The second derivative [src]
    /           2\
2*x*\-201 - 90*x /
$$2 x \left(- 90 x^{2} - 201\right)$$
The third derivative [src]
   /         2\
-6*\67 + 90*x /
$$- 6 \cdot \left(90 x^{2} + 67\right)$$
The graph
Derivative of (5x-9x³)(8+x²)