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Beliebt Rechnen >

(\partial)/(\partial y)(3x^2(5x+7y))

Lösung

\frac{\partial}{\partial y} (3 x^{2} (5 x + 7 y))

Lösung

21 x^{2}

Schritte zur Lösung

\frac{\partial}{\partial y} (3 x^{2} (5 x + 7 y))

Behandle

x

als Konstante

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 x^{2} \frac{\partial}{\partial y} (5 x + 7 y)

Wende die Summen-/Differenzregel an:

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

= 3 x^{2} (\frac{\partial}{\partial y} (5 x) + \frac{\partial}{\partial y} (7 y))

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

\frac{\partial}{\partial y} (7 y) = 7

= 3 x^{2} (0 + 7)

Vereinfache

= 21 x^{2}

Beliebte Beispiele

derivative f(x)=x^3-6x^2+9x

d er i v a t i v e f (x) = x^{3} - 6 x^{2} + 9 x

limit as x approaches pi/4 of tan(2x)

x \to \frac{π}{4} lim (tan (2 x))

integral of (7x+3)/(sqrt(x))

\int \frac{7 x + 3}{x} d x

limit as x approaches infinity of x^4

x \to \infty lim (x^{4})

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