In AHL 5.15, students expand their knowledge of derivatives to include more complex trigonometric functions:
To find the derivative of $y = \tan(3x)$, we use the chain rule: $\frac{dy}{dx} = \sec^2(3x) \cdot 3 = 3\sec^2(3x)$
For exponential and logarithmic functions with any base $a$:
When $a = e$ (Euler's number), these simplify to the familiar forms: $\frac{d}{dx}(e^x) = e^x$ and $\frac{d}{dx}(\ln x) = \frac{1}{x}$
The derivatives of inverse trigonometric functions are also covered:
Do not forget to use the chain rule on these standard derivatives!
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