Mister Exam

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The derivative of the function/ 3cos^2x

Derivative of 3cos^2x

The solution

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     2   
3*cos (x)

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

3*cos(x)^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \cos{\left(x \right)}$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(x \right)}$ :
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  The result of the chain rule is:
  
  $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
So, the result is: $- 6 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /   2         2   \
6*\sin (x) - cos (x)/

$$6 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)$$

Simplify

The third derivative [src]

24*cos(x)*sin(x)

$$24 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph

Derivative of 3cos^2x