derivative of tanx
sec^2x
The derivative of tan(x) can be found using the quotient rule:
Let y = tan(x)
Then y’ = (sec^2(x))(1) – (tan(x))(sec^2(x))(1)
Simplifying this expression, we get:
y’ = sec^2(x) – tan^2(x)
Since 1 + tan^2(x) = sec^2(x) (by the Pythagorean identity), we can replace tan^2(x) with sec^2(x) – 1:
y’ = sec^2(x) – (sec^2(x) – 1)
y’ = 1
Therefore, the derivative of tan(x) is simply 1.
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