Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 8^x
Derivative of (x-2)^2*(x-4)+5
Derivative of (x-1)/2
Derivative of sin(x)*sin(x)
Integral of d{x}:
sin(2*x)^(2)
Identical expressions
sin(two *x)^(two)
sinus of (2 multiply by x) to the power of (2)
sinus of (two multiply by x) to the power of (two)
sin(2*x)(2)
sin2*x2
sin(2x)^(2)
sin(2x)(2)
sin2x2
sin2x^2
Similar expressions
y=sin(2*x)^2
sin(2x^2+1)

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

Derivative of 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

The graph

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