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Derivative of (5x-6)cosx-5sin-8

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

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The solution

You have entered [src]
(5*x - 6)*cos(x) - 5*sin(x) - 8
$$\left(\left(5 x - 6\right) \cos{\left(x \right)} - 5 \sin{\left(x \right)}\right) - 8$$
(5*x - 6)*cos(x) - 5*sin(x) - 8
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

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

        1. The derivative of sine is cosine:

        So, 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]
-(5*x - 6)*sin(x)
$$- \left(5 x - 6\right) \sin{\left(x \right)}$$
The second derivative [src]
-(5*sin(x) + (-6 + 5*x)*cos(x))
$$- (\left(5 x - 6\right) \cos{\left(x \right)} + 5 \sin{\left(x \right)})$$
The third derivative [src]
-10*cos(x) + (-6 + 5*x)*sin(x)
$$\left(5 x - 6\right) \sin{\left(x \right)} - 10 \cos{\left(x \right)}$$