Derivative of tan x
sec^2 x
The derivative of tan x can be found using the quotient rule of differentiation. Recall that tan x = sin x / cos x. Applying the quotient rule, we have:
d/dx (tan x) = [(cos x)(d/dx sin x) – (sin x)(d/dx cos x)] / (cos x)^2
Using the fact that d/dx sin x = cos x and d/dx cos x = -sin x, we obtain:
d/dx (tan x) = [(cos x)(cos x) – (sin x)(-sin x)] / (cos x)^2
Simplifying, we get:
d/dx (tan x) = sec^2 x
Therefore, the derivative of tan x is sec^2 x.
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