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Derivative of:
Derivative of (x+2)
Derivative of 1+x
Derivative of (sqrt(x)-1)/sqrt(x^2-x-1)
Derivative of e^x*cos(x)
Identical expressions
cos^ two (x)- three
co sinus of e of squared (x) minus 3
co sinus of e of to the power of two (x) minus three
cos2(x)-3
cos2x-3
cos²(x)-3
cos to the power of 2(x)-3
cos^2x-3
Similar expressions
cos^2(x)+3

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

Derivative of cos^2(x)-3

The solution

You have entered [src]

   2       
cos (x) - 3

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

cos(x)^2 - 3

Detail solution

Differentiate $\cos^{2}{\left(x \right)} - 3$ term by term:
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:
  
  $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
4. The derivative of the constant $-3$ is zero.
The result is: $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*cos(x)*sin(x)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

8*cos(x)*sin(x)

$$8 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify