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Example 19 Find the derivative of f from the first principle, where f is given by (i) f(x) = (2x 3)/(x − 2) Let f (x) = (2x 3)/(x − 2) We need to find Derivative of f(x) ie f' (x) We know that f'(x) = lim┬(h→0) f⁡〖(x h) − f(x)〗/h Here, f (x) = (2x 3)/(x − 2) So,We know that the derivative of tan x is sec 2 x (ie) d/dx (tan x) = sec 2 x According to the chain rule, d/dx tan 2x = sec 2 (2x) d/dx (2x)The derivative of tan−1x is 1 1 x2 (for why, see note below) So, applying the chain rule, we get d dx (tan−1u) = 1 1 u2 ⋅ du dx In this question u = 2x, so we get d dx (tan−12x) = 1 1 (2x)2 ⋅ d dx (2x) = 2 1 4x2 Derivative Rules For Trigonometric Functions Mile 22 find the derivative of tan(2x+3)