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

Gregory Emery 2021-12-17 Answered
What is the derivative of tan(2x) ?
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Orlando Paz
Answered 2021-12-18 Author has 42 answers
Assuming that you know the derivative rule: ddx(tanx)=sec2(x)
ddx(tan(2x)) will simply be sec2(2x)ddx(2x) according to the chain rule.
Then ddx(tan(2x))=2sec2(2x)
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)

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Jack Maxson
Answered 2021-12-19 Author has 25 answers
The first thing to realize is that we're dealing with a composite function f(g(x)), where
f(x)=tanx and g(x)=2x
When we differentiate a composite function, we use the Chain Rule
f(g(x))g(x)
From the definition of tangent and an application of the Quotient Rule, we know that f(x)=sec2x
We 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 as
2sec2(2x)
Hope this helps!

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