Differentiation of tan x

The function y=tan x can be differentiated easily.

Since tan x = sin x / cos x, we can replace the trigonometry identity with this.

Since we have a function divided by a function we can use the quotient rule, and the top part of the fraction becomes f(x) = sin x, and the derivative of sin x is cos x.

The bottom part of the fraction becomes g(x) = cos x, and the derivative of cos x = -sin x

Using the quotient rule, we substitute all the known terms to give the expression above.

Finally, you get this simple looking expression.

Using the standard trigonometry identity shown above, we can substitute it into the top part of our fraction.

The derivative of tan x is therefore this.

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