(\partial)/(\partial u)(({g}(u,v,w))(uv+w^2))

Lösung

\frac{\partial}{\partial u} ((g (u, v, w)) (uv + w^{2}))

\frac{\partial}{\partial u} (g (u, v, w)) (uv + w^{2}) + v g (u, v, w)

Schritte zur Lösung

\frac{\partial}{\partial u} ((g (u, v, w)) (uv + w^{2}))

Behandle

v, w

als Konstanten

Wende die Produktregel an:

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

f = g (u, v, w), g = uv + w^{2}

= \frac{\partial}{\partial u} (g (u, v, w)) (uv + w^{2}) + \frac{\partial}{\partial u} (uv + w^{2}) g (u, v, w)

\frac{\partial}{\partial u} (uv + w^{2}) = v

= \frac{\partial}{\partial u} (g (u, v, w)) (uv + w^{2}) + v g (u, v, w)

e x p an d C (- 3, - 4) P (7, - 1)

e x p an d (2 e^{3 x} + 6 e^{3 x} x + e^{x} + e^{x} x)^{2}

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

e x p an d \frac{x ^{2} - 7 x + 9}{( x - 1 ) ^{2} ( x + 2 )}

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