Mister Exam

Derivative of 2*sin(2*x)

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

from to

Piecewise:

The solution

You have entered [src]
2*sin(2*x)
2sin(2x)2 \sin{\left(2 x \right)}
d             
--(2*sin(2*x))
dx            
ddx2sin(2x)\frac{d}{d x} 2 \sin{\left(2 x \right)}
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: 4cos(2x)4 \cos{\left(2 x \right)}


The answer is:

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

The graph
02468-8-6-4-2-1010-1010
The first derivative [src]
4*cos(2*x)
4cos(2x)4 \cos{\left(2 x \right)}
The second derivative [src]
-8*sin(2*x)
8sin(2x)- 8 \sin{\left(2 x \right)}
The third derivative [src]
-16*cos(2*x)
16cos(2x)- 16 \cos{\left(2 x \right)}
The graph
Derivative of 2*sin(2*x)