Given-that-y-5x-2-3-show-that-when-x-2-6-5-d-2-y-dx-2-125-8-

Question Number 69765 by Rio Michael last updated on 27/Sep/19

G i v e n t h a t y = \sqrt{5 x^{2} + 3}, s h o w t h a t w h e n x^{2} = \frac{6}{5}, \frac{d^{2} y}{{d x}^{2}} = \frac{125}{8}

Answered by MJS last updated on 27/Sep/19

y = \sqrt{5 x^{2} + 3}

\frac{d y}{d x} = y^{'} = \frac{5 x}{\sqrt{5 x^{2} + 3}}

\frac{d^{2} y}{{d x}^{2}} = y^{″} = \frac{15}{{(5 x^{2} + 3)}^{3 / 2}} \overset{x^{2} = \frac{6}{5}}{=} \frac{5}{9}

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