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1/2sin2x
The derivative of the function/ 1/2sin2x

Derivative of 1/2sin2x

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
sin(2*x)
--------
   2
sin⁡(2x)2\frac{\sin{\left(2 x \right)}}{2} 
d /sin(2*x)\
--|--------|
dx\   2    /
ddxsin⁡(2x)2\frac{d}{d x} \frac{\sin{\left(2 x \right)}}{2}
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let u=2xu = 2 x.

    2. The derivative of sine is cosine:

      ddusin⁡(u)=cos⁡(u)\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}

    3. Then, apply the chain rule. Multiply by ddx2x\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: xx goes to 11

        So, the result is: 22

      The result of the chain rule is:

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

    So, the result is: cos⁡(2x)\cos{\left(2 x \right)}

The answer is:

cos⁡(2x)\cos{\left(2 x \right)}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
cos(2*x)
cos⁡(2x)\cos{\left(2 x \right)}
Simplify
The second derivative [src] 
-2*sin(2*x)
−2sin⁡(2x)- 2 \sin{\left(2 x \right)}
Simplify
The third derivative [src] 
-4*cos(2*x)
−4cos⁡(2x)- 4 \cos{\left(2 x \right)}
Simplify
The graph
Derivative of 1/2sin2x
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