What is the derivative of (x^2/(1-y^2)) ?

The derivative of (x^2/(1-y^2)) is (2x(1-y^2)+2x^2y\frac{dy)/(dx)}{(1-y^2)^2}

What is the first derivative of (x^2/(1-y^2)) ?

The first derivative of (x^2/(1-y^2)) is (2x(1-y^2)+2x^2y\frac{dy)/(dx)}{(1-y^2)^2}

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\frac{d}{d x} (\frac{x ^{2}}{1 - y ^{2}})

\frac{2 x ( 1 - y ^{2} ) + 2 x ^{2} y \frac{d y}{d x}}{( 1 - y ^{2} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{1 - 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} ) ( 1 - y ^{2} ) - \frac{d}{d x} ( 1 - y ^{2} ) x ^{2}}{( 1 - y ^{2} ) ^{2}}

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

\frac{d}{d x} (1 - y^{2}) = - 2 y \frac{d y}{d x}

= \frac{2 x ( 1 - y ^{2} ) - ( - 2 y \frac{d y}{d x} ) x ^{2}}{( 1 - y ^{2} ) ^{2}}

Simplify

= \frac{2 x ( 1 - y ^{2} ) + 2 x ^{2} y \frac{d y}{d x}}{( 1 - y ^{2} ) ^{2}}

(x + 3) (x - 5)^{7}

x \to + 0 lim (\frac{x ^{2} - 5}{x - 2})

\frac{d y}{1 - y ^{2}} = d x

\frac{d y}{d t} = \frac{8 t y}{t ^{2} + 1}, y (0) = - 2

\int 15 x^{2} d x

What is the derivative of (x^2/(1-y^2)) ?
The derivative of (x^2/(1-y^2)) is (2x(1-y^2)+2x^2y\frac{dy)/(dx)}{(1-y^2)^2}
What is the first derivative of (x^2/(1-y^2)) ?
The first derivative of (x^2/(1-y^2)) is (2x(1-y^2)+2x^2y\frac{dy)/(dx)}{(1-y^2)^2}