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Derivative Proof of tan(x)

Derivative proof of tan(x)

We can prove this derivative by using the derivatives of sin and cos, as well as quotient rule.

Write tangent in terms of sine and cosine

Take the derivative of both sides

Use Quotient Rule

Simplify

Use the Pythagorean identity for sine and cosine

and simplify

Derivative proofs of csc(x), sec(x), and cot(x)

The derivative of these trig functions can be obtained easily from the Qoutient Rule using the reciprocals of sin(x), cos(x), and tan(x).