Derivative of tan(x)
sec^2u du
The derivative of tangent function can be found by using the quotient rule of differentiation.
Let y = tan(x), then we have:
y = sin(x) / cos(x)
To find the derivative of y, we use the quotient rule which states that:
(d/dx) [f(x) / g(x)] = [f'(x)*g(x) – g'(x)*f(x)] / [g(x)]^2
Applying this formula here, we get:
y’ = [(cos(x)*cos(x) – (-sin(x)*sin(x))) / (cos(x))^2]
Simplifying the above expression, we get:
y’ = sec^2(x)
Therefore, the derivative of tan(x) is sec^2(x).
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