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NSW Y12 Maths - Advanced Trig Functions Differentiation of Trig Functions

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Differentiation of Trig Functions Theory

For \(y=\sin x \quad \dfrac{d y}{d x}=\cos x\)\\ For \(y=\cos x \quad \dfrac{d y}{d x}=-\sin x\)\\ For \(y=\tan x \quad \dfrac{d y}{d x}=\sec ^2 x\)\\ For \(y=\operatorname{cosec} x \dfrac{d y}{d x}=-\operatorname{cosec} x \cot x\)\\ For \(y=\sec x \quad \dfrac{d y}{d x}=\sec x \tan x\)\\ For \(y=\cot x \quad \dfrac{d y}{d x}=-\operatorname{cosec}^2 x\)\\ \begin{multicols}{2} \textbf{Example 1}\\%24809 Differentiate \(\sin ({x^2} + 1)\)\\ \textbf{Example 1 solution}\\ $\begin{aligned} y &=\sin \left(x^{2}+1\right) \\ y^{\prime} &=2 x \cos \left(x^{2}+1\right)  \end{aligned}$\\ \columnbreak \textbf{Example 2}\\%31081 Differentiate \(x\sec x\)\\ \textbf{Example 2 solution}\\ $\begin{aligned} \frac{d}{dx}(x\sec x) &= \frac{d}{dx}(x)\times \sec x + \frac{d}{dx} (\sec x)\times x\\&= 1\times \sec x + x\sec x\tan x\\&= \sec x(1 + x\tan x) \end{aligned}$\\ \end{multicols}

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Videos

Videos relating to Differentiation of Trig Functions.

  • Differentiation of Trig Functions - Video - Differentiating trigonometric functions using the chain rule : Exam Solutions

  • Differentiation of Trig Functions - Video - Differentiation - sin(x) and cos(x)

  • Differentiation of Trig Functions - Video - Derivative Rules with TRIG functions

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