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Derivative of:
Derivative of x^2*cos(2*x)
Derivative of ((x-1)/(x+1))^4
Derivative of (x-1)/(2*x+3)
Derivative of sqrt(x)^2-2*x
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=5cos^2x
f(x) equally 5 co sinus of e of squared x
f(x)=5cos2x
fx=5cos2x
f(x)=5cos²x
f(x)=5cos to the power of 2x
fx=5cos^2x

The derivative of the function/ f(x)=5cos^2x

Derivative of f(x)=5cos^2x

The solution

You have entered [src]

     2   
5*cos (x)

$$5 \cos^{2}{\left(x \right)}$$

5*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: $- 10 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

$- 5 \sin{\left(2 x \right)}$

The answer is:

$- 5 \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-10*cos(x)*sin(x)

$$- 10 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

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

$$10 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)$$

Simplify

3-я производная [src]

40*cos(x)*sin(x)

$$40 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The third derivative [src]

40*cos(x)*sin(x)

$$40 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify