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Beliebt Rechnen >

(\partial)/(\partial x)(x^2y^3+6xyz-2yz)

Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} + 6 x yz - 2 yz)

Lösung

2 x y^{3} + 6 yz

Schritte zur Lösung

\frac{\partial}{\partial x} (x^{2} y^{3} + 6 x yz - 2 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} (6 x yz) - \frac{\partial}{\partial x} (2 yz)

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

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

\frac{\partial}{\partial x} (2 yz) = 0

= 2 y^{3} x + 6 yz - 0

Vereinfache

= 2 x y^{3} + 6 yz

Beliebte Beispiele

integral of 1/(1+sin^2(x))

\int \frac{1}{1 + sin ^{2} ( x )} d x

(\partial)/(\partial x)(7xe^{x^2}+y^2)

\frac{\partial}{\partial x} (7 x e^{x^{2}} + y^{2})

integral of (23)/((x^2-1)^2)

\int \frac{23}{( x ^{2} - 1 ) ^{2}} d x

sum from n=1 to infinity of (n-1)/(5n-1)

n = 1 \sum \infty \frac{n - 1}{5 n - 1}

(x^2+2y^')y^{''}+2xy^'=0

(x^{2} + 2 y^{^{'}}) y^{^{''}} + 2 x y^{^{'}} = 0