derv tan(x)
sec^2(x)
I believe you meant to ask for the derivative of tan(x).
The derivative of tan(x) can be found using the quotient rule.
Recall that the quotient rule states that if f(x) = u(x)/v(x), then f'(x) = [u'(x)v(x) – u(x)v'(x)] / v(x)^2.
Using this rule and the fact that tan(x) = sin(x) / cos(x), we can calculate the derivative of tan(x) as follows:
tan(x) = sin(x) / cos(x)
tan'(x) = [cos(x) * cos(x) – (-sin(x) * sin(x))] / cos(x)^2 (apply quotient rule and chain rule)
tan'(x) = [cos^2(x) + sin^2(x)] /cos^2(x)
tan'(x) = 1 / cos^2(x)
tan'(x) = sec^2(x)
Therefore, the derivative of tan(x) is sec^2(x).
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