Derivative of 4/cosx

You have entered [src]

  4   
------
cos(x)

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

4/cos(x)

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: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
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:
  
  $\frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}$
So, the result is: $\frac{4 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /         2   \
  |    2*sin (x)|
4*|1 + ---------|
  |        2    |
  \     cos (x) /
-----------------
      cos(x)

$$\frac{4 \left(\frac{2 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1\right)}{\cos{\left(x \right)}}$$

Simplify

The third derivative [src]

  /         2   \       
  |    6*sin (x)|       
4*|5 + ---------|*sin(x)
  |        2    |       
  \     cos (x) /       
------------------------
           2            
        cos (x)

$$\frac{4 \left(\frac{6 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 5\right) \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of 4/cosx

The graph:

Piecewise:

The solution