What is the derivative of-(x^2/(y^2)) ?

The derivative of-(x^2/(y^2)) is -(2x(-x\frac{dy)/(dx)+y)}{y^3}

What is the first derivative of-(x^2/(y^2)) ?

The first derivative of-(x^2/(y^2)) is -(2x(-x\frac{dy)/(dx)+y)}{y^3}

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Cancel

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

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

m \to 0 lim (\frac{m}{m ^{2} + 4 m})

\int e^{4 x - 3} d x

\int \frac{( x - 1 )}{( x - 2 ) ( x - 3 )} d x

x \to 2 lim (∣ x ∣)

x \to 0 lim (x + 5)

What is the derivative of-(x^2/(y^2)) ?
The derivative of-(x^2/(y^2)) is -(2x(-x\frac{dy)/(dx)+y)}{y^3}
What is the first derivative of-(x^2/(y^2)) ?
The first derivative of-(x^2/(y^2)) is -(2x(-x\frac{dy)/(dx)+y)}{y^3}