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Derivative of:
Derivative of (x+3)^4
Derivative of (x-2)^3
Derivative of sqrt(x^2-1)
Derivative of ln(x)/x
Integral of d{x}:
2*sin(2*x)
Graphing y =:
2*sin(2*x)
Limit of the function:
2*sin(2*x)
Identical expressions
two *sin(two *x)
2 multiply by sinus of (2 multiply by x)
two multiply by sinus of (two multiply by x)
2sin(2x)
2sin2x
Similar expressions
sinx+1/2*sin2x
y=ln^2sin2x
5*sin6x-x^2*sin2x

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

Derivative of 2sin(2x)

The solution

You have entered [src]

2*sin(2*x)

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

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

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
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:
  
  $2 \cos{\left(2 x \right)}$
So, the result is: $4 \cos{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4*cos(2*x)

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

Simplify

The second derivative [src]

-8*sin(2*x)

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

Simplify

The third derivative [src]

-16*cos(2*x)

$$- 16 \cos{\left(2 x \right)}$$

Simplify

The graph

Derivative of 2*sin(2*x)