Question

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write in notebook ​

Answer 1

Given Expression,

$\sf y = 2 log_{e}( {x}^{2} )$

Differentiating w.r.t x,

$\longrightarrow \sf \: \dfrac{dy}{dx} = \dfrac{d \{2 log_{e}( {x}^{2} ) \} }{dx} \\ \\ \longrightarrow \sf \: \dfrac{dy}{dx} = 2\dfrac{d \{log_{e}( {x}^{2} ) \} }{dx} \\ \\ \longrightarrow \sf \: \dfrac{dy}{dx} = 2 \times \dfrac{1}{ {x}^{2} } \times \dfrac{d( {x}^{2} )}{dx} \\ \\ \longrightarrow \sf \: \dfrac{dy}{dx} = \dfrac{2}{ {x}^{2} } \times 2x \\ \\ \longrightarrow \boxed{ \boxed {\sf \: \dfrac{dy}{dx} = \dfrac{4}{x} }}$

Derivative of the above expression is 4/x.

Formula Used :

$\sf \: \dfrac{d \{ log(x) \} }{dx} = \dfrac{1}{x}$