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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\int \frac{cos ( x )}{cos ^{2} ( x )} d x

d er i v a t i v e y = \frac{x ^{3} + 3 x ^{2} - 5 x + 2}{3}

y^{^{'}} - 8 y^{3} = 0

\int \frac{1}{2 x - 1 - 4 2 x - 1} d x

\int x^{1.1} (\frac{1}{3 x} - 1) d x