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Maclaurin series is the Taylor series expansion of an algebraic expression using derivatives, at point 0.

We find all the derivatives of f(x) and find their values at x = 0. Substitute them in the above series expansion formula or polynomial.

In the derviative f''''(x) we will have a term tan x, hence f''''(0) = 0, as tan0=0. All even numbered derivatives will be 0.

tan x = tan 0 + x * 1 + x²/2! 0 + x³/3! * 2 + x^4/4! * 0 + ....

tan x = x + 2x³/3! + .....

We find all the derivatives of f(x) and find their values at x = 0. Substitute them in the above series expansion formula or polynomial.

In the derviative f''''(x) we will have a term tan x, hence f''''(0) = 0, as tan0=0. All even numbered derivatives will be 0.

tan x = tan 0 + x * 1 + x²/2! 0 + x³/3! * 2 + x^4/4! * 0 + ....

tan x = x + 2x³/3! + .....