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Beliebt Rechnen >

(\partial)/(\partial x)(xe^y+x^4y+y^3)

Lösung

\frac{\partial}{\partial x} (x e^{y} + x^{4} y + y^{3})

Lösung

e^{y} + 4 x^{3} y

Schritte zur Lösung

\frac{\partial}{\partial x} (x e^{y} + x^{4} y + y^{3})

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

= \frac{\partial}{\partial x} (x e^{y}) + \frac{\partial}{\partial x} (x^{4} y) + \frac{\partial}{\partial x} (y^{3})

\frac{\partial}{\partial x} (x e^{y}) = e^{y}

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

\frac{\partial}{\partial x} (y^{3}) = 0

= e^{y} + 4 y x^{3} + 0

Vereinfache

= e^{y} + 4 x^{3} y

Beliebte Beispiele

derivative of ln(x^2+y^4)

\frac{d}{d x} (ln (x^{2} + y^{4}))

laplacetransform 4cos(5t)

l a pl a ce t r an s f or m 4 cos (5 t)

y^{^{'}} + y = 3

y^'=6xsqrt(9-y^2)

y^{^{'}} = 6 x 9 - y^{2}

y^'=1+x+y^2+xy^2

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