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

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

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

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

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

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

Solution steps

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

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

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