(\partial)/(\partial x)(x^2y^3+4xyz-3yz)

Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} + 4 x yz - 3 yz)

2 x y^{3} + 4 yz

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} + 4 x yz - 3 yz)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2} y^{3}) + \frac{\partial}{\partial x} (4 x yz) - \frac{\partial}{\partial x} (3 yz)

\frac{\partial}{\partial x} (x^{2} y^{3}) = 2 y^{3} x

\frac{\partial}{\partial x} (4 x yz) = 4 yz

\frac{\partial}{\partial x} (3 yz) = 0

= 2 y^{3} x + 4 yz - 0

Vereinfache

= 2 x y^{3} + 4 yz

l a pl a ce t r an s f or m 6 e^{- 3} - t^{2} + 2 t - 8

x y^{^{'}} + 2 y = - 2 sin (x)

\int 10 sin^{3} (x co) s^{7} x d x

s im pl i f y \frac{4 x}{x}

\int \frac{x}{2 x - 6} d x