What is the derivative of xy^'-y ?

The derivative of xy^'-y is y^'+'x(dy)/(dx)y^{'-1}-(dy)/(dx)

What is the first derivative of xy^'-y ?

The first derivative of xy^'-y is y^'+'x(dy)/(dx)y^{'-1}-(dy)/(dx)

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

y^{'} +' x \frac{d y}{d x} y^{' - 1} - \frac{d y}{d x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

= y^{^{^{'}}} +^{^{'}} x \frac{d y}{d x} y^{^{^{'}} - 1} - \frac{d y}{d x}

\int \frac{1}{x ^{2} + x - 6} d x

9 x^{2}

\frac{d}{d x} (ln (x^{2} - 5 x + 2))

\int \frac{ln ( 2 )}{x ^{2}} d x

y^{^{'}} = \frac{( 3 t ^{2} - e ^{t} )}{( 2 y - 5 )}, y (0) = 1

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