Derivative of cos2x

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cos(2*x)

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

d           
--(cos(2*x))
dx

\frac{d}{d x} \cos{\left(2 x \right)}

Transform

Detail solution

Let $u = 2 x$ .
The derivative of cosine is negative sine:

$\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $2$
The result of the chain rule is:

$- 2 \sin{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*sin(2*x)

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

Simplify

The second derivative [src]

-4*cos(2*x)

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

Simplify

The third derivative [src]

8*sin(2*x)

8 \sin{\left(2 x \right)}

Simplify

The graph