(\partial)/(\partial x)(x/(sqrt(x^2+y^3)))

Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{3}})

\frac{y ^{3}}{( x ^{2} + y ^{3} ) x ^{2} + y ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{3}})

Behandle

y

als Konstante

Wende die Quotientenregel an:

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

= \frac{\frac{\partial}{\partial x} ( x ) x ^{2} + y ^{3} - \frac{\partial}{\partial x} ( x ^{2} + y ^{3} ) x}{( x ^{2} + y ^{3} ) ^{2}}

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (x^{2} + y^{3}) = \frac{x}{x ^{2} + y ^{3}}

= \frac{1 \cdot x ^{2} + y ^{3} - \frac{x}{x ^{2} + y ^{3}} x}{( x ^{2} + y ^{3} ) ^{2}}

Vereinfache

\frac{1 \cdot x ^{2} + y ^{3} - \frac{x}{x ^{2} + y ^{3}} x}{( x ^{2} + y ^{3} ) ^{2}} : \frac{y ^{3}}{( x ^{2} + y ^{3} ) x ^{2} + y ^{3}}

= \frac{y ^{3}}{( x ^{2} + y ^{3} ) x ^{2} + y ^{3}}

y^{^{'}} + 7 = e^{7 x + y - 5}, y (0) = 5

a re a \frac{1}{4} x^{2} - 1, 0, 2, 8

y = 2 sin (x)

\frac{d}{d x} (arctan (\frac{x}{2}))

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