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Beliebt Rechnen >

(\partial)/(\partial x)(6xy+5yz+xz-48)

Lösung

\frac{\partial}{\partial x} (6 x y + 5 yz + x z - 48)

Lösung

6 y + z

Schritte zur Lösung

\frac{\partial}{\partial x} (6 x y + 5 yz + x z - 48)

Behandle

y, z

als Konstanten

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (6 x y) + \frac{\partial}{\partial x} (5 yz) + \frac{\partial}{\partial x} (x z) - \frac{\partial}{\partial x} (48)

\frac{\partial}{\partial x} (6 x y) = 6 y

\frac{\partial}{\partial x} (5 yz) = 0

\frac{\partial}{\partial x} (x z) = z

\frac{\partial}{\partial x} (48) = 0

= 6 y + 0 + z - 0

Vereinfache

= 6 y + z

Beliebte Beispiele

16y^{''}+152y^'+361y=0,y(0)=9,y^'(0)=2

16 y^{^{''}} + 152 y^{^{'}} + 361 y = 0, y (0) = 9, y^{^{'}} (0) = 2

(\partial)/(\partial y)(ln(1+x^2+y))

\frac{\partial}{\partial y} (ln (1 + x^{2} + y))

integral of (18)/((x^2-1)^2)

\int \frac{18}{( x ^{2} - 1 ) ^{2}} d x

y^'+7x^{-1}y=x^2

y^{^{'}} + 7 x^{- 1} y = x^{2}

derivative 10arcsin(e^{x/2})

d er i v a t i v e 10 arcsin (e^{\frac{x}{2}})