Question

Differentiate 2x²+3/√x with respect to x​

Answer 1

$y = \frac{2x {}^{2} + 3 }{ \sqrt{x} }$

$\frac{dy}{dx} = \: \frac{VU {}^{1} - UV {}^{1} }{V {}^{2} }$

$\frac{dy}{dx} = \frac{ \sqrt{x}. \frac{d(2x {}^{2} + 3) }{dx} - 2x {}^{2} + 3. \frac{d( \sqrt{x} )}{dx} }{ (\sqrt{x}) {}^{2} }$

$\frac{dy}{dx} = \frac{ \sqrt{x} .(4x + 0) - 2x {}^{2} + 3.( \frac{1}{2 \sqrt{x} }) }{( \sqrt{x}) {}^{2} }$

$\frac{dy}{dx} = \frac{ \sqrt{x} \: . \: 4x \: - \: 2x {}^{2} + 3 \: . \: \frac{1}{2 \sqrt{x} } }{ (\sqrt{x}) {}^{2} }$

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