(\partial)/(\partial y)((x^2+y)(x-y^2))

Lösung

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

- 3 y^{2} - 2 x^{2} y + x

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2} + y, g = x - y^{2}

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

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

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

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

Vereinfache

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

= - 3 y^{2} - 2 x^{2} y + x

\frac{d}{d x} (7^{x})

d er i v a t i v e y = ln (3 x + 1) e^{x^{2} + 4}

\int \frac{4 x ^{2} - 3 x + 2}{4 x ^{2} - 4 x + 3} d x

\int_{1}^{2} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

f a c t or 2 cos (x) + cos^{2} (x)