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Beliebt Rechnen >

(\partial)/(\partial y)(5xy^2+x^2)

Lösung

\frac{\partial}{\partial y} (5 x y^{2} + x^{2})

Lösung

10 x y

Schritte zur Lösung

\frac{\partial}{\partial y} (5 x y^{2} + x^{2})

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial y} (5 x y^{2}) + \frac{\partial}{\partial y} (x^{2})

\frac{\partial}{\partial y} (5 x y^{2}) = 10 x y

\frac{\partial}{\partial y} (x^{2}) = 0

= 10 x y + 0

Vereinfache

= 10 x y

Beliebte Beispiele

t^2y^{''}+ty^'+64y=0

t^{2} y^{^{''}} + t y^{^{'}} + 64 y = 0

\frac{d}{d v} (\frac{m}{v})

derivative 1-2x

d er i v a t i v e 1 - 2 x

limit as t approaches 1+of 4/((t-1)^3)

t \to 1 + lim (\frac{4}{( t - 1 ) ^{3}})

(\partial)/(\partial x)((x^2+y^2+z^2)^{3/2})

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