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y=(sin(4*x-1))^3

Derivative of y=(sin(4*x-1))^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   3         
sin (4*x - 1)
$$\sin^{3}{\left(4 x - 1 \right)}$$
d /   3         \
--\sin (4*x - 1)/
dx               
$$\frac{d}{d x} \sin^{3}{\left(4 x - 1 \right)}$$
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                      
12*sin (4*x - 1)*cos(4*x - 1)
$$12 \sin^{2}{\left(4 x - 1 \right)} \cos{\left(4 x - 1 \right)}$$
The second derivative [src]
   /     2                  2          \              
48*\- sin (-1 + 4*x) + 2*cos (-1 + 4*x)/*sin(-1 + 4*x)
$$48 \left(- \sin^{2}{\left(4 x - 1 \right)} + 2 \cos^{2}{\left(4 x - 1 \right)}\right) \sin{\left(4 x - 1 \right)}$$
The third derivative [src]
    /       2                  2          \              
192*\- 7*sin (-1 + 4*x) + 2*cos (-1 + 4*x)/*cos(-1 + 4*x)
$$192 \left(- 7 \sin^{2}{\left(4 x - 1 \right)} + 2 \cos^{2}{\left(4 x - 1 \right)}\right) \cos{\left(4 x - 1 \right)}$$
The graph
Derivative of y=(sin(4*x-1))^3