derivative of (y-sqrt(x)^{1/2})

Lösung

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

\frac{2 x ^{\frac{1}{2}} \frac{d y}{d x} - 1}{4 x ^{\frac{1}{2}} ( y - x ) ^{\frac{1}{2}}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

\frac{1}{2 ( y - x ) ^{\frac{1}{2}}} (\frac{d y}{d x} - \frac{1}{2 x ^{\frac{1}{2}}}) : \frac{2 x ^{\frac{1}{2}} \frac{d y}{d x} - 1}{4 x ^{\frac{1}{2}} ( y - x ) ^{\frac{1}{2}}}

= \frac{2 x ^{\frac{1}{2}} \frac{d y}{d x} - 1}{4 x ^{\frac{1}{2}} ( y - x ) ^{\frac{1}{2}}}

\int (9 - x^{2})^{- \frac{3}{2}} d x

l a pl a ce t r an s f or m - 2 e^{t}

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

\frac{\partial}{\partial y} (7 e^{x} sin (y))

f (x) = - \frac{5}{x ^{3}}