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

Derivative of sin(2*x)

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

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The solution

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

  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)}

The answer is:

2cos⁡(2x)2 \cos{\left(2 x \right)}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2*cos(2*x)
2cos⁡(2x)2 \cos{\left(2 x \right)}
Simplify
The second derivative [src] 
-4*sin(2*x)
−4sin⁡(2x)- 4 \sin{\left(2 x \right)}
Simplify
The third derivative [src] 
-8*cos(2*x)
−8cos⁡(2x)- 8 \cos{\left(2 x \right)}
Simplify
The graph
Derivative of sin(2*x)
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