Mister Exam

Derivative of -sin2x

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           
ddx(sin(2x))\frac{d}{d x} \left(- \sin{\left(2 x \right)}\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: 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 -sin2x