Find the first three nonzero terms of the Maclaurin series for the tangent function by computing its higher-order derivatives.

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Maclaurin Series for Tangent

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Find the first three nonzero terms of the Maclaurin series for \(\tan x\).

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What you need first

Derivatives of basic trigonometric functions
The chain rule
The product rule
Evaluating trigonometric functions at zero
Factorials

What this problem tests

Tests the ability to repeatedly apply the product and chain rules accurately, and to construct a power series from derivative values.

Finding the Maclaurin series of the tangent function is a standard exercise in Calculus II, demonstrating the rapid growth in complexity of higher-order derivatives for quotients of trigonometric functions.

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