What is (d^2)/(dx^2)(x/y) ?

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

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(d^2)/(dx^2)(x/y)

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

- \frac{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{x}{y})

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

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

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

\int 3 x^{2} ln (x^{2} + 5) d x

x \to 0 lim (x [ln (x)]^{2})

\int \frac{( 1 + e ^{x} )}{e ^{x}} d x

x \to 1 lim ((x - 1)^{x - 1})

\int \frac{1}{θ} d θ

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