Mister Exam

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The derivative of the function/ 1/2sin2x

Derivative of 1/2sin2x

The solution

You have entered [src]

sin(2*x)
--------
   2

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

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

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

cos(2*x)

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

Simplify

The second derivative [src]

-2*sin(2*x)

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

Simplify

The third derivative [src]

-4*cos(2*x)

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

Simplify

The graph

Derivative of 1/2sin2x