derivative of (sqrt(25-x^2-y^2)/y)

Lösung

\frac{d}{d x} (\frac{25 - x ^{2} - y ^{2}}{y})

\frac{x ^{2} \frac{d y}{d x} - x y - 25 \frac{d y}{d x}}{y ^{2} - x ^{2} - y ^{2} + 25}

Schritte zur Lösung

\frac{d}{d x} (\frac{25 - x ^{2} - y ^{2}}{y})

Wende die Quotientenregel an:

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

= \frac{\frac{d}{d x} ( 25 - x ^{2} - y ^{2} ) y - \frac{d y}{d x} 25 - x ^{2} - y ^{2}}{y ^{2}}

\frac{d}{d x} (25 - x^{2} - y^{2}) = - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 25}

= \frac{( - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 25} ) y - \frac{d y}{d x} 25 - x ^{2} - y ^{2}}{y ^{2}}

Vereinfache

\frac{( - \frac{x + y \frac{d y}{d x}}{- x ^{2} - y ^{2} + 25} ) y - \frac{d y}{d x} 25 - x ^{2} - y ^{2}}{y ^{2}} : \frac{x ^{2} \frac{d y}{d x} - x y - 25 \frac{d y}{d x}}{y ^{2} - x ^{2} - y ^{2} + 25}

= \frac{x ^{2} \frac{d y}{d x} - x y - 25 \frac{d y}{d x}}{y ^{2} - x ^{2} - y ^{2} + 25}

x \to \frac{π}{2} lim (tan (\frac{x}{2}))

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

t a y l or tan (x)

\frac{\partial}{\partial x} (e^{8 x - 200})

\frac{d}{d z ( t )} (\frac{( x - 1 ) z ( t )}{2 z ( t ) - 4 t + 1})