Mister Exam

Derivative of cos(1-2x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
cos(1 - 2*x)
cos(12x)\cos{\left(1 - 2 x \right)}
Detail solution
  1. Let u=12xu = 1 - 2 x.

  2. The derivative of cosine is negative sine:

    dducos(u)=sin(u)\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}

  3. Then, apply the chain rule. Multiply by ddx(12x)\frac{d}{d x} \left(1 - 2 x\right):

    1. Differentiate 12x1 - 2 x term by term:

      1. The derivative of the constant 11 is zero.

      2. 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: 2-2

      The result is: 2-2

    The result of the chain rule is:

    2sin(2x1)- 2 \sin{\left(2 x - 1 \right)}


The answer is:

2sin(2x1)- 2 \sin{\left(2 x - 1 \right)}

The graph
02468-8-6-4-2-10105-5
The first derivative [src]
-2*sin(-1 + 2*x)
2sin(2x1)- 2 \sin{\left(2 x - 1 \right)}
The second derivative [src]
-4*cos(-1 + 2*x)
4cos(2x1)- 4 \cos{\left(2 x - 1 \right)}
The third derivative [src]
8*sin(-1 + 2*x)
8sin(2x1)8 \sin{\left(2 x - 1 \right)}
The graph
Derivative of cos(1-2x)