Question

find the second derivative of y(x)=x^-3/2

Answer 1

$</p><p></p><p>\sf \rightarrow \quad y(x) = {x}^{ - \frac{3}{2} } \\ \\ \sf \rightarrow \quad y'(x) = \frac{d}{dx} ( {x}^{ - \frac{3}{2} } ) \\ \\ \sf \rightarrow \quad y'(x) = \frac{ -3 }{2} \times {x}^{ \frac{ - 5}{2} } \\ \\ \sf \rightarrow \quad y'(x) = - \frac{3}{2 {x}^{2} \sqrt{x} } \\ \\ \sf \rightarrow \quad y''(x) = \frac{d}{dx} \bigg( \frac{ - 3}{2 {x}^{2} \sqrt{x} } \bigg) \\ \\ \sf \rightarrow \quad y''(x) = - \frac{3}{2} \times - \frac{5}{2} \times {x}^{ - \frac{7}{2} } \\ \\ \sf \rightarrow \quad y''(x) = \frac{15}{4x^{3}\sqrt{x}} </p><p>$