Question

derivative with respect to x for the function:
$\sqrt{5x {}^{2} - 10x + 3 }$
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Answer 1

$\bf{ \orange{ \underline{ \underline{ \orange{Question :}}}}} \\ \\ \\ \bull \: \: \sf \: Differentiate \: \: the \: \: given \: \: function \: \: with \: \: respect \: \: to \: \: x \\ \\ \\ \bf{ \orange{ \underline{ \underline{ \orange{ Step-by-step explanation :}}}}} \\ \\ \\ y = \big(\sqrt{5x {}^{2} - 10x + 3 }\big) \\ \\ \\ \longrightarrow \ln y = \ln {\big(5 {x}^{2} - 10x + 3\big)}^{ \frac{1}{2} } \\ \\ \\ \longrightarrow \ln y = \frac{1}{2} \ln\big(5 {x}^{2} - 10x + 3\big) \\ \\ \\ \longrightarrow \frac{d}{dx} \big( \ln y\big) = \frac{1}{2} \frac{d}{dx} \ln\big(5 {x}^{2} - 10x + 3\big) \\ \\ \\ \longrightarrow \frac{1}{y} \frac{dy}{dx} = \frac{1}{2} \frac{1}{\big(5 {x}^{2} - 10x + 3\big)} \big(10x - 10\big) \\ \\ \\ \longrightarrow \frac{dy}{dx} = \frac{ 5\big(x - 1\big)\sqrt{5 {x}^{2} - 10x + 3 } }{5 {x}^{2} - 10x + 3}$