Mister Exam

Derivative of (5*x-6)*cos(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
(5*x - 6)*cos(x)
$$\left(5 x - 6\right) \cos{\left(x \right)}$$
(5*x - 6)*cos(x)
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 the constant is zero.

      The result is:

    ; to find :

    1. The derivative of cosine is negative sine:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
5*cos(x) - (5*x - 6)*sin(x)
$$- \left(5 x - 6\right) \sin{\left(x \right)} + 5 \cos{\left(x \right)}$$
The second derivative [src]
-(10*sin(x) + (-6 + 5*x)*cos(x))
$$- (\left(5 x - 6\right) \cos{\left(x \right)} + 10 \sin{\left(x \right)})$$
The third derivative [src]
-15*cos(x) + (-6 + 5*x)*sin(x)
$$\left(5 x - 6\right) \sin{\left(x \right)} - 15 \cos{\left(x \right)}$$
The graph
Derivative of (5*x-6)*cos(x)