d/dx tan x
sec^2 x
The derivative of the tangent function is found by using the quotient rule of differentiation, which states that if f(x) = u(x)/v(x), then:
f'(x) = [v(x)u'(x) – u(x)v'(x)] / [v(x)]^2
Applying this rule to f(x) = tan x, we get:
f'(x) = [(sec x)^2 (1)] / [(cos x)^2] = (sec x)^2 / (cos x)^2
Thus, the derivative of tan x with respect to x is (sec x)^2 / (cos x)^2.
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