Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^-1
Derivative of 2*x^5
Derivative of sin(2*x^2+3)
Derivative of f(x)=5
Identical expressions
one - two *cos(x)^(two)
1 minus 2 multiply by co sinus of e of (x) to the power of (2)
one minus two multiply by co sinus of e of (x) to the power of (two)
1-2*cos(x)(2)
1-2*cosx2
1-2cos(x)^(2)
1-2cos(x)(2)
1-2cosx2
1-2cosx^2
Similar expressions
1+2*cos(x)^(2)
1-2*cosx^(2)

The derivative of the function/ 1-2*cos(x)^(2)

Derivative of 1-2*cos(x)^(2)

The solution

You have entered [src]

         2   
1 - 2*cos (x)

$$1 - 2 \cos^{2}{\left(x \right)}$$

1 - 2*cos(x)^2

Detail solution

Differentiate $1 - 2 \cos^{2}{\left(x \right)}$ term by term:
1. The derivative of the constant $1$ is zero.
2. 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: $4 \sin{\left(x \right)} \cos{\left(x \right)}$
The result is: $4 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

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

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]

4*cos(x)*sin(x)

$$4 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

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

$$4 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$

Simplify

The third derivative [src]

-16*cos(x)*sin(x)

$$- 16 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify