Question

read this attachment ​

Answer 1

FORMULAE OF DIFFERENTIATION ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

→$\tt{\dfrac{d}{dx} x^{n} = nx^{n-1}}$

→$\tt{\dfrac{d}{dx} (constant) = 0} ⠀$

→ $\tt{\dfrac{d}{dx} kf(x) = k. \dfrac{d}{dx} f(x)}$

→ $\tt{\dfrac{d}{dx} (u+v) = \dfrac{du}{dx} + \dfrac{dv}{dx} }$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

→$\tt{\dfrac{d}{dx} (u-v) = \dfrac{du}{dx} - \dfrac{dv}{dx}}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀

→ $\tt{\dfrac{d}{dx} (u.v) = u \dfrac{dv}{dx} + v \dfrac{du}{dx}}$ ⠀⠀⠀⠀⠀⠀

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

→$\tt{\dfrac{d}{dx} (Cos x) = - sin x}$

→$\tt{\dfrac{d}{dx} (Sin x) = Cos x}$

→$\tt{\dfrac{d}{dx} (Tan x) = Sec^2 x}$

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

→$\tt{\dfrac{d}{dx} (Sec x) = Sec x. Tan x}$

→$\tt{\dfrac{d}{dx} (Cosec x) = - Cosec x. Cot x}$ ⠀

→$\tt{\dfrac{d}{dx} log_{e}(x) = \dfrac{1}{x}}$

→ $\tt{\dfrac{d}{dx} e^x = e^x}$ ⠀⠀⠀⠀⠀

→$\tt{\dfrac{d}{dx} a^x = a^{x} . log_{e}{a}}$

Answer 2

Answer:

A radical is an atom, molecule, or ion that has an unpaired valence electron. A notable example of a radical is the hydroxil ( HO.) group, a molecule that has one unpaired electron on the oxygen atom.