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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

e x p an d (c + 4 e^{2} - 3 s^{4})^{2}

e x p an d \frac{x y}{( x + y ) ^{2}}

e x p an d (x^{2} + 1) e^{3 x}

e x p an d - \frac{2 ( - 9 x cos ( 9 x ) + sin ( 9 x ) )}{2187}

e x p an d (1 - 2 x + x^{2})^{5}