IB Maths AA 5.9 Notes

Trigonometric derivatives

This section extends differentiation to a wider range of functions. The key idea is that these derivatives should be recognised quickly, then combined with the chain rule whenever the input is not just $x$.

The main trigonometric derivatives are:

• $\frac{d}{dx}(\tan x)=\sec^2 x$
• $\frac{d}{dx}(\sec x)=\sec x\tan x$
• $\frac{d}{dx}(\cosec x)=-\cosec x\cot x$
• $\frac{d}{dx}(\cot x)=-\cosec^2 x$

These should be memorised, as they appear often in differentiation questions.

Find the derivative of $y=\tan x+\sec x$.

$\frac{dy}{dx}=\sec^2 x+\sec x\tan x$

Find the derivative of $y=4\cot x-3\cosec x$.

$\frac{dy}{dx}=-4\cosec^2 x+3\cosec x\cot x$.