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sin^3(2x+1)

Derivative of sin^3(2x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3         
sin (2*x + 1)
$$\sin^{3}{\left(2 x + 1 \right)}$$
d /   3         \
--\sin (2*x + 1)/
dx               
$$\frac{d}{d x} \sin^{3}{\left(2 x + 1 \right)}$$
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                      
6*sin (2*x + 1)*cos(2*x + 1)
$$6 \sin^{2}{\left(2 x + 1 \right)} \cos{\left(2 x + 1 \right)}$$
The second derivative [src]
   /     2                 2         \             
12*\- sin (1 + 2*x) + 2*cos (1 + 2*x)/*sin(1 + 2*x)
$$12 \left(- \sin^{2}{\left(2 x + 1 \right)} + 2 \cos^{2}{\left(2 x + 1 \right)}\right) \sin{\left(2 x + 1 \right)}$$
The third derivative [src]
   /       2                 2         \             
24*\- 7*sin (1 + 2*x) + 2*cos (1 + 2*x)/*cos(1 + 2*x)
$$24 \left(- 7 \sin^{2}{\left(2 x + 1 \right)} + 2 \cos^{2}{\left(2 x + 1 \right)}\right) \cos{\left(2 x + 1 \right)}$$
The graph
Derivative of sin^3(2x+1)