1. Soalan a: Cari \(\frac{dy}{dx}\) bagi fungsi \(y = (6x^2 + 4x)^4\) dan nilai \(y\) bila \(x = \frac{1}{2}\). 2. Gunakan kaedah rantai untuk membeza fungsi kuasa komposit. Formula asas: $$\frac{d}{dx}[f(g(x))] = f'(g(x)) \cdot g'(x)$$ 3. Tetapkan \(u = 6x^2 + 4x\), maka \(y = u^4\). 4. Derivatif \(y\) terhadap \(x\) adalah: $$\frac{dy}{dx} = 4u^3 \cdot \frac{du}{dx}$$ 5. Hitung \(\frac{du}{dx}\): $$\frac{du}{dx} = 12x + 4$$ 6. Jadi, $$\frac{dy}{dx} = 4(6x^2 + 4x)^3 (12x + 4)$$ 7. Cari nilai \(y\) bila \(x = \frac{1}{2}\): $$u = 6\left(\frac{1}{2}\right)^2 + 4\left(\frac{1}{2}\right) = 6\cdot \frac{1}{4} + 2 = 1.5 + 2 = 3.5$$ $$y = (3.5)^4 = 150.0625$$ 8. Soalan b i: Bezakan fungsi \(5x^3 + 4x^2 + 3x + 6\). Gunakan aturan kuasa: $$\frac{d}{dx}[x^n] = nx^{n-1}$$ Derivatif: $$\frac{d}{dx}[5x^3] = 15x^2$$ $$\frac{d}{dx}[4x^2] = 8x$$ $$\frac{d}{dx}[3x] = 3$$ $$\frac{d}{dx}[6] = 0$$ Jadi, $$\frac{dy}{dx} = 15x^2 + 8x + 3$$ 9. Soalan b ii: Bezakan fungsi \((2x + 4)^6\). Gunakan kaedah rantai: $$u = 2x + 4$$ $$\frac{dy}{dx} = 6u^5 \cdot \frac{du}{dx} = 6(2x + 4)^5 \cdot 2 = 12(2x + 4)^5$$