Find the derivative of the function y frac 1 x - SS3 Mathematics Differential Calculus (Differentiation) Question
Find the derivative of the function \(y = \frac{1}{x}\)
A
\(- \frac{1}{x^{2}}\)
B
\(\frac{1}{x^{2}}\)
C
\(\frac{1}{2x}\)
D
\(- 2x^{2}\)
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Correct Option: A
\[\frac{dy}{dx} = \frac{v\frac{du}{dx} - u\frac{dv}{dx}}{v^{2}}\]
\[u = 1,\ \ \ \ \ \ \ \ \ \ \ \ v = x\]
\[\frac{du}{dx} = 0,\ \ \ \ \ \ \ \ \ \frac{dv}{dx} = 1\]
\(\frac{dy}{dx} = \frac{x(0) - 1(1)}{x^{2}} = - \frac{1}{x^{2}}\)
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