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Derivative of:
Derivative of 6
Derivative of x^2+3x
Derivative of sinx/cosx
Derivative of sqrt(1-x)
Identical expressions
sin(two *x)^(three)
sinus of (2 multiply by x) to the power of (3)
sinus of (two multiply by x) to the power of (three)
sin(2*x)(3)
sin2*x3
sin(2x)^(3)
sin(2x)(3)
sin2x3
sin2x^3
Similar expressions
3^(sin2x^3+4sin2x)
y=sin(2x)^3*cos8x^5

The derivative of the function/ sin(2*x)^(3)

Derivative of sin(2*x)^(3)

The solution

You have entered [src]

   3     
sin (2*x)

$$\sin^{3}{\left(2 x \right)}$$

sin(2*x)^3

Detail solution

Let $u = \sin{\left(2 x \right)}$ .
Apply the power rule: $u^{3}$ goes to $3 u^{2}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(2 x \right)}$ :
1. Let $u = 2 x$ .
2. The derivative of sine is cosine:
  
  $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $2$
  The result of the chain rule is:
  
  $2 \cos{\left(2 x \right)}$
The result of the chain rule is:

$6 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}$

The answer is:

$6 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2              
6*sin (2*x)*cos(2*x)

$$6 \sin^{2}{\left(2 x \right)} \cos{\left(2 x \right)}$$

Simplify

The second derivative [src]

   /     2             2     \         
12*\- sin (2*x) + 2*cos (2*x)/*sin(2*x)

$$12 \left(- \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}\right) \sin{\left(2 x \right)}$$

Simplify

The third derivative [src]

   /       2             2     \         
24*\- 7*sin (2*x) + 2*cos (2*x)/*cos(2*x)

$$24 \left(- 7 \sin^{2}{\left(2 x \right)} + 2 \cos^{2}{\left(2 x \right)}\right) \cos{\left(2 x \right)}$$

Simplify

The graph

Derivative of sin(2*x)^(3)