differentiate tan(x)

1) Let's find the domain of

\tan (x)

⇥ For the expression

\tan (x)

to be defined, the following condition is necessary:

\cos (x) \neq 0

⇥From cos(θ) ≠

0

, we deduce: θ ≠

\frac{π}{2} + k π

, k ∈ ℤ

⇥Solution obtained:

x \neq \frac{π}{2} + k π

⇥Domain of definition:

{x \neq \frac{π}{2} + k π, k \in ℤ}

2) Let's differentiate:

\frac{d}{d x} (\tan (x))

ⓘ The derivative of

\tan (x)

\frac{1}{{\cos (x)}^{2}}

\frac{d}{d x} (\tan (x))

\frac{1}{{\cos (x)}^{2}}

▶Derivative:

\frac{1}{{\cos (x)}^{2}}

, for

\cos (x) \neq 0

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