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Derivative of:
Derivative of ln(x+3)^3
Derivative of cot(1/x)
Derivative of cos(x)-1
Derivative of cos(3*x)^(2)
Identical expressions
cos(three *x)^(two)
co sinus of e of (3 multiply by x) to the power of (2)
co sinus of e of (three multiply by x) to the power of (two)
cos(3*x)(2)
cos3*x2
cos(3x)^(2)
cos(3x)(2)
cos3x2
cos3x^2
Similar expressions
-9*sin(3*x)/(cos(3*x))^2
y=sin^5(3x^2-1)*cos3x^2

The derivative of the function/ cos(3*x)^(2)

Derivative of cos(3*x)^(2)

The solution

You have entered [src]

   2     
cos (3*x)

$$\cos^{2}{\left(3 x \right)}$$

cos(3*x)^2

Detail solution

Let $u = \cos{\left(3 x \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(3 x \right)}$ :
1. Let $u = 3 x$ .
2. The derivative of cosine is negative sine:
  
  $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
3. 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 result of the chain rule is:

$- 6 \sin{\left(3 x \right)} \cos{\left(3 x \right)}$
Now simplify:

$- 3 \sin{\left(6 x \right)}$

The answer is:

$- 3 \sin{\left(6 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-6*cos(3*x)*sin(3*x)

$$- 6 \sin{\left(3 x \right)} \cos{\left(3 x \right)}$$

Simplify

The second derivative [src]

   /   2           2     \
18*\sin (3*x) - cos (3*x)/

$$18 \left(\sin^{2}{\left(3 x \right)} - \cos^{2}{\left(3 x \right)}\right)$$

Simplify

The third derivative [src]

216*cos(3*x)*sin(3*x)

$$216 \sin{\left(3 x \right)} \cos{\left(3 x \right)}$$

Simplify

The graph

Derivative of cos(3*x)^(2)