What is (d^2}{dx^2}(-\frac{2x)/y) ?

The answer to (d^2}{dx^2}(-\frac{2x)/y) is (2(x\frac{d^2y)/(dx^2)y+2(dy)/(dx)(-x(dy)/(dx)+y))}{y^3}

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(d^2}{dx^2}(-\frac{2x)/y)

\frac{d ^{2}}{d x ^{2}} (- \frac{2 x}{y})

\frac{2 ( x \frac{d ^{2} y}{d x ^{2}} y + 2 \frac{d y}{d x} ( - x \frac{d y}{d x} + y ) )}{y ^{3}}

Solution steps

\frac{d ^{2}}{d x ^{2}} (- \frac{2 x}{y})

\frac{d}{d x} (- \frac{2 x}{y}) = - \frac{2 ( y - x \frac{d y}{d x} )}{y ^{2}}

= \frac{d}{d x} - \frac{2 ( y - x \frac{d y}{d x} )}{y ^{2}}

\frac{d}{d x} - \frac{2 ( y - x \frac{d y}{d x} )}{y ^{2}} = \frac{2 ( x \frac{d ^{2} y}{d x ^{2}} y + 2 \frac{d y}{d x} ( - x \frac{d y}{d x} + y ) )}{y ^{3}}

= \frac{2 ( x \frac{d ^{2} y}{d x ^{2}} y + 2 \frac{d y}{d x} ( - x \frac{d y}{d x} + y ) )}{y ^{3}}

x \to a lim ([f (x) g (x)])

\frac{( - 2 s + 21 )}{( s ^{2} - 8 s + 20 )}

\frac{d}{d x} (x (x^{3} + 7)^{4})

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 4)

y (θ) = \frac{π}{3} sin (θ)

What is (d^2}{dx^2}(-\frac{2x)/y) ?
The answer to (d^2}{dx^2}(-\frac{2x)/y) is (2(x\frac{d^2y)/(dx^2)y+2(dy)/(dx)(-x(dy)/(dx)+y))}{y^3}