derivative of (x+1/(x^2-y+1))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

\frac{d}{d x} (x + 1) = 1

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

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

Vereinfache

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

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

y^{^{''}} - 6 y^{^{'}} + 9 = 0

s l o p e (- 5) (0.7)

\int \frac{1}{e ^{v}} d v

\frac{\partial}{\partial y} (\frac{x ^{2} + y ^{2}}{x + y})

\int 2 x^{2 x} (ln (x) + 1) d x