(\partial)/(\partial x)(({f}(x,y))(xy-y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

f = f (x, y), g = x y - y^{2}

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

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

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

e x p an d \frac{2 π}{365} (x - 114)

e x p an d \frac{( 8 - x ^{2} - y ^{2} ) ^{3}}{3}

e x p an d \frac{( s + 2 )}{( s + 3 ) \cdot ( s + 6 ) \cdot ( s + 8 )}

s im pl i f y 1 0^{10} δ (x - 9)

e x p an d \frac{1000}{( S + 2 ) ( S + 3 ) ( S + 5 )}