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Derivative of 18*sin^2(x)-2

Function f() - derivative -N order at the point
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The solution

You have entered [src]
      2       
18*sin (x) - 2
$$18 \sin^{2}{\left(x \right)} - 2$$
18*sin(x)^2 - 2
Detail solution
  1. Differentiate term by term:

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

      1. Let .

      2. Apply the power rule: goes to

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

        1. The derivative of sine is cosine:

        The result of the chain rule is:

      So, 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]
36*cos(x)*sin(x)
$$36 \sin{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
   /   2         2   \
36*\cos (x) - sin (x)/
$$36 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$
The third derivative [src]
-144*cos(x)*sin(x)
$$- 144 \sin{\left(x \right)} \cos{\left(x \right)}$$