Question

find the derivative with respect to x of function √2-3x²​

Answer 1

Answer:

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Answer 2

Given expression,

$\sf y = \sqrt{2 - {3x}^{2} }$

Differentiating w.r.t x,

$\longrightarrow \sf \: \dfrac{dy}{dx} = \dfrac{d( \sqrt{2 - {3x}^{2} }) }{dx} \\ \\ \longrightarrow \sf \: \dfrac{dy}{dx} = \dfrac{1}{\sqrt{2 - {3x}^{2}}} \times \dfrac{d(2 - 3 {x}^{2} )}{dx} \\ \\ \longrightarrow \sf \: \dfrac{dy}{dx} = \dfrac{1}{\sqrt{2 - {3x}^{2}}} \bigg \{ \dfrac{d(2 )}{dx} - \dfrac{d(3x {}^{2} )}{dx} \bigg \} \\ \\ \longrightarrow \sf \: \dfrac{dy}{dx} = - \dfrac{6x}{\sqrt{2 - {3x}^{2}}}$

The derivative of the above expression is -6x/√2 - 3x^2.

Formula Used :

$\sf \dfrac{d( \sqrt{x} )}{dx} = \dfrac{1}{2 \sqrt{x} }$