Question

Deferentation of y=log/e,(x^2)​

Answer 1

Questions:-

• Deferentation of y=2log/e,(x^2)

Solution:-

$\rm \longrightarrow y = 2 \: log_{e}( {x}^{2} )$

Now , we have to differentiate the above expression.

$\rm \longrightarrow \dfrac{dy}{dx} = \dfrac{d \bigg(2 \: log_{e}( {x}^{2} ) \bigg )}{dx}$

$\rm \longrightarrow \dfrac{dy}{dx} = 2 \times \dfrac{d \bigg( \: log_{e}( {x}^{2} ) \bigg )}{dx}$

Now by using chain rule :-

$\rm \longrightarrow \dfrac{dy}{dx} = 2 \times \dfrac{ 1}{ {x}^{2} } \times \dfrac{d( {x}^{2}) }{dx}$

$\rm \longrightarrow \dfrac{dy}{dx} = 2 \times \dfrac{ 1}{ {x}^{2} } \times \: {2x }$

$\rm \longrightarrow \dfrac{dy}{dx} = 2 \times \dfrac{ 1}{ {x} } \times \: {2}$

$\rm \longrightarrow \dfrac{dy}{dx} = \dfrac{ 4}{ x }$

• Answer :- 4/x

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