(\partial)/(\partial y)(xsqrt(1+y^3))

Lösung

\frac{\partial}{\partial y} (x 1 + y^{3})

\frac{3 x y ^{2}}{2 1 + y ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial y} (x 1 + y^{3})

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= x \frac{\partial}{\partial y} (1 + y^{3})

Wende die Kettenregel an:

\frac{1}{2 1 + y ^{3}} \frac{\partial}{\partial y} (1 + y^{3})

= \frac{1}{2 1 + y ^{3}} \frac{\partial}{\partial y} (1 + y^{3})

\frac{\partial}{\partial y} (1 + y^{3}) = 3 y^{2}

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

Vereinfache

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

= \frac{3 x y ^{2}}{2 1 + y ^{3}}

l a pl a ce t r an s f or m 4 t \cdot sin (3 t)

\frac{x y ^{^{'}}}{y ^{2}} sin (\frac{x}{y}) = \frac{1}{y} sin (\frac{x}{y})

\frac{\partial}{\partial y} (5 x^{2} + 2 y^{2})

\int 13 cos^{3} (x) d x

\frac{d P}{d t} = \frac{P}{5} - \frac{P ^{2}}{75}, P (0) = 5