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Derivative of sin^1(2x+3)^3

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

The graph:

from to

Piecewise:

The solution

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   1         
sin (2*x + 3)
$$\sin^{1}{\left(2 x + 3 \right)}$$
sin(2*x + 3)^1
Detail solution
  1. Let .

  2. Apply the power rule: goes to

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

    1. Let .

    2. The derivative of sine is cosine:

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

      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:

      The result of the chain rule is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
2*cos(2*x + 3)
$$2 \cos{\left(2 x + 3 \right)}$$
The second derivative [src]
-4*sin(3 + 2*x)
$$- 4 \sin{\left(2 x + 3 \right)}$$
The third derivative [src]
-8*cos(3 + 2*x)
$$- 8 \cos{\left(2 x + 3 \right)}$$