Mister Exam

Derivative of sin(2*x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

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