Question

Formulas of differentiation​

Answer 1

AnswEr:

Formulae of differentiation :⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

★ $\sf{\dfrac{d}{dx} x^{n} = nx^{n-1}}$

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★ $\sf{\dfrac{d}{dx} (constant) = 0}$

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★ $\sf{\dfrac{d}{dx} kf(x) = k. \dfrac{d}{dx} f(x)}$

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★ $\sf{\dfrac{d}{dx} (u+v) = \dfrac{du}{dx} + \dfrac{dv}{dx}}$

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★ $\sf{\dfrac{d}{dx} (u-v) = \dfrac{du}{dx} - \dfrac{dv}{dx}}$

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★ $\sf{\dfrac{d}{dx} (u.v) = u \dfrac{dv}{dx} + v \dfrac{du}{dx}}$

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★ $\sf{\dfrac{d}{dx} (\dfrac{u}{v}) = \dfrac{v \dfrac{du}{dx} - u \dfrac{dv}{dx}}{v^2}}$

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★ $\sf{\dfrac{d}{dx} (Cos x) = - sin x}$

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★ $\sf{\dfrac{d}{dx} (Sin x) = Cos x}$

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★ $\sf{\dfrac{d}{dx} (Tan x) = Sec^2 x}$

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★ $\sf{\dfrac{d}{dx} (Cot x) = - Cosec^2 x}$

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★ $\sf{\dfrac{d}{dx} (Sec x) = Sec x. Tan x}$

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★ $\sf{\dfrac{d}{dx} (Cosec x) = - Cosec x. Cot x}$

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★ $\sf{\dfrac{d}{dx} log_{e}(x) = \dfrac{1}{x}}$

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★ $\sf{\dfrac{d}{dx} e^x = e^x}$

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★ $\sf{\dfrac{d}{dx} a^x = a^{x} . log_{e}{a}}$

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$\rule{200}2$

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Examples :

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1). $\sf{\dfrac{d}{dx}(2x^2 + 3x^3 )}$

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→ $\sf{\dfrac{d}{dx} (2x)^2 + \dfrac{d}{dx} (3x)^3}$

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→ $\sf{2(2x) + 3(3x^2)}$

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→ 4x + 9x² ( Answer )

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2). $\sf{\dfrac{d}{dx} 2x^2}$

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→ $\sf{2 \dfrac{d}{dx} x^2}$

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→ $\sf{2(2x)}$

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→ 4x ( Answer )