Finding d/dx[tan(x)]

Calculus 1 · Axiom Academy

Deriving the rule from scratch using the quotient rule. We know how to differentiate and . Use those, together with the quotient rule, to find . Show that it simplifies to . Nice work. You built from the ground up — no memorized rule, just , , the quotient rule, and one identity. Rewrite first: turns an unfamiliar derivative into a quotient you already know how to differentiate. Quotient rule: gives the numerator . One identity closes it: , so the result collapses to . The same recipe — rewrite as a quotient, differentiate, simplify with a Pythagorean identity — also produces the derivatives of , , and .

This is the written version of the interactive lesson above. See the full Calculus 1 course.