What is the derivative of tan⁡(2x) ?

Question

Orlando Paz · Accepted Answer

Assuming that you know the derivative rule:

\frac{d}{d x} (\tan x) = \sec^{2} (x)

\frac{d}{d x} (\tan (2 x))

will simply be

\sec^{2} (2 x) \cdot \frac{d}{d x} (2 x)

according to the chain rule.
Then

\frac{d}{d x} (\tan (2 x)) = 2 \sec^{2} (2 x)

If you want to easily understand chain rule, just remember my tips: take the normal derivative of the outside (ignoring whatever is inside the parenthesis) and then multiply it by the derivative of the inside (stuff inside the parenthesis)

Jack Maxson · Accepted Answer

The first thing to realize is that we&#039;re dealing with a composite function f(g(x)), wheref(x)=tan⁡x and g(x)=2xWhen we differentiate a composite function, we use the Chain Rulef′(g(x))⋅g′(x)From the definition of tangent and an application of the Quotient Rule, we know that f′(x)=sec2xWe also know that g′(x)=2. Now, we have everything we need to plug into the Chain Rule:sec2(2x)⋅2, which can be rewritten as2sec2(2x)Hope this helps!

What is the derivative of \tan(2x) ?

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