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$1 . \dfrac{d}{dx}(c ) = o \\[3mm] 2. \dfrac{d}{dx}(x) = 1 \\[3mm] 3. \dfrac{d}{dx} (x^n) = nx^{n- 1} \\[3mm] 4. \dfrac{d}{dx}(u \pm v) = \dfrac{du}{dx} \pm \dfrac{dv}{dx} \\[3mm] 5. \dfrac{d}{dx}(cu) = c\dfrac{du}{dx} \\[3mm] 6. \dfrac{d}{dx}(uv) = u \dfrac{dv}{dx} + v \dfrac{du}{dx} \\[3mm] 7. \dfrac{d}{dx}\left(\dfrac{u}{v} \right) = \dfrac{v \dfrac{du}{dx}- u \dfrac{dv}{dx}}{v^2}(\text{quotient rule}) \\[3mm] 8. \dfrac{d}{dx}(u^n) = nu^{n- 1} \dfrac{du}{dx} \\[3mm] 9. \dfrac{d}{dx}(yu, v) = \dfrac{dv}{dx} \left(\dfrac{du}{dx}, y \right) \\ 10. \dfrac{d}{dx} (u, v) = \dfrac{dv}{dx} \left(\dfrac{du}{dx}, v \right) (\text{Chain Rule}) \dfrac{du}{dx} = \dfrac{du}{dv} \dfrac{dv}{dx} \\ \text{Another similar formula is given by} \dfrac{du}{dx} = \dfrac{\dfrac{du}{dv}}{\dfrac{dx}{dv}}$

Derivative Formula