Mister Exam

Derivative of sec

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
sec(x)
$$\sec{\left(x \right)}$$
sec(x)
Detail solution
  1. Rewrite the function to be differentiated:

  2. Let .

  3. Apply the power rule: goes to

  4. Then, apply the chain rule. Multiply by :

    1. The derivative of cosine is negative sine:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
sec(x)*tan(x)
$$\tan{\left(x \right)} \sec{\left(x \right)}$$
The second derivative [src]
/         2   \       
\1 + 2*tan (x)/*sec(x)
$$\left(2 \tan^{2}{\left(x \right)} + 1\right) \sec{\left(x \right)}$$
The third derivative [src]
/         2   \              
\5 + 6*tan (x)/*sec(x)*tan(x)
$$\left(6 \tan^{2}{\left(x \right)} + 5\right) \tan{\left(x \right)} \sec{\left(x \right)}$$
The graph
Derivative of sec