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

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Produktregel an:

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

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

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

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

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

e x p an d e^{2 x} (3 x + 2)

e x p an d \frac{( y ^{2} + 2 y - 3 ) ^{2}}{16 ( y + 1 ) ^{2}}

e x p an d \frac{b ^{2}}{( n - 1 ) \cdot s ^{2}}

s im pl i f y (- 8 t^{3} + 68 t^{2} - 204 t + 207) \cdot (- 1.2)

e x p an d f (s) [(1 + e^{2 t})^{2}]