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y=sin(5x+3)^3

Derivative of y=sin(5x+3)^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3         
sin (5*x + 3)
$$\sin^{3}{\left(5 x + 3 \right)}$$
sin(5*x + 3)^3
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                      
15*sin (5*x + 3)*cos(5*x + 3)
$$15 \sin^{2}{\left(5 x + 3 \right)} \cos{\left(5 x + 3 \right)}$$
The second derivative [src]
   /     2                 2         \             
75*\- sin (3 + 5*x) + 2*cos (3 + 5*x)/*sin(3 + 5*x)
$$75 \left(- \sin^{2}{\left(5 x + 3 \right)} + 2 \cos^{2}{\left(5 x + 3 \right)}\right) \sin{\left(5 x + 3 \right)}$$
The third derivative [src]
    /       2                 2         \             
375*\- 7*sin (3 + 5*x) + 2*cos (3 + 5*x)/*cos(3 + 5*x)
$$375 \left(- 7 \sin^{2}{\left(5 x + 3 \right)} + 2 \cos^{2}{\left(5 x + 3 \right)}\right) \cos{\left(5 x + 3 \right)}$$
The graph
Derivative of y=sin(5x+3)^3