Derivative of cos3x

You have entered [src]

cos(3*x)

$$\cos{\left(3 x \right)}$$

d           
--(cos(3*x))
dx

$$\frac{d}{d x} \cos{\left(3 x \right)}$$

Transform

Detail solution

Let $u = 3 x$ .
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 $\frac{d}{d x} 3 x$ :
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: $3$
The result of the chain rule is:

$- 3 \sin{\left(3 x \right)}$

The answer is:

$- 3 \sin{\left(3 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3*sin(3*x)

$$- 3 \sin{\left(3 x \right)}$$

Simplify

The second derivative [src]

-9*cos(3*x)

$$- 9 \cos{\left(3 x \right)}$$

Simplify

The third derivative [src]

27*sin(3*x)

$$27 \sin{\left(3 x \right)}$$

Simplify

The graph