Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 1/3*x^3
Derivative of x^2/(x^2+1)
Derivative of x*sqrt(3-x)
Derivative of (x^2+25)/x
Limit of the function:
sin(2*x)^2
Identical expressions
y=sin(two *x)^ two
y equally sinus of (2 multiply by x) squared
y equally sinus of (two multiply by x) to the power of two
y=sin(2*x)2
y=sin2*x2
y=sin(2*x)²
y=sin(2*x) to the power of 2
y=sin(2x)^2
y=sin(2x)2
y=sin2x2
y=sin2x^2
Similar expressions
sin(2x^2+1)

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

Derivative of y=sin(2*x)^2

The solution

You have entered [src]

   2     
sin (2*x)

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

d /   2     \
--\sin (2*x)/
dx

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

Transform

Detail solution

Let $u = \sin{\left(2 x \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
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:

$4 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$
Now simplify:

$2 \sin{\left(4 x \right)}$

The answer is:

$2 \sin{\left(4 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4*cos(2*x)*sin(2*x)

$$4 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$

Simplify

The second derivative [src]

  /   2           2     \
8*\cos (2*x) - sin (2*x)/

$$8 \left(- \sin^{2}{\left(2 x \right)} + \cos^{2}{\left(2 x \right)}\right)$$

Simplify

The third derivative [src]

-64*cos(2*x)*sin(2*x)

$$- 64 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$

Simplify

3-я производная [src]

-64*cos(2*x)*sin(2*x)

$$- 64 \sin{\left(2 x \right)} \cos{\left(2 x \right)}$$

Simplify

The graph

Derivative of y=sin(2*x)^2