Derivative of tan x
sec^2 x
The derivative of tan x can be found using the quotient rule. Let y = tan x.
y’ = d/dx(tan x)
Using the quotient rule:
y’ = [(sec x)^2 * d/dx(x) – (tan x)(d/dx(sec x)^2)] / (sec x)^4
Simplifying:
y’ = [(sec x)^2 – (tan x)(2 sec x tan x)] / (sec x)^4
y’ = sec x / (cos x)^2
Therefore, the derivative of tan x is sec x / (cos x)^2.
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