# Derivative of sin^3(2x)

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

from to

### The solution

You have entered [src]
   3
sin (2*x)
$$\sin^{3}{\left(2 x \right)}$$
d /   3     \
--\sin (2*x)/
dx           
$$\frac{d}{d x} \sin^{3}{\left(2 x \right)}$$
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. 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:

The result of the chain rule is:

The result of the chain rule is:

The graph
The first derivative [src]
     2
6*sin (2*x)*cos(2*x)
$$6 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}$$
The second derivative [src]
   /     2             2     \
12*\- sin (2*x) + 2*cos (2*x)/*sin(2*x)
$$12 \left(- \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}\right) \sin{\left(2 x \right)}$$
The third derivative [src]
   /       2             2     \
24*\- 7*sin (2*x) + 2*cos (2*x)/*cos(2*x)
$$24 \left(- 7 \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}\right) \cos{\left(2 x \right)}$$
The graph 