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Beliebt Rechnen >

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

Lösung

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

Lösung

3 (15 x^{2} + 14 x y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Entferne die Konstante:

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

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = 5 x + 7 y

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

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

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

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

Multipliziere aus

2 x (5 x + 7 y) + 5 x^{2} : 15 x^{2} + 14 x y

= 3 (15 x^{2} + 14 x y)

Beliebte Beispiele

tan(x)(dy)/(dx)=y

tan (x) \frac{d y}{d x} = y

limit as x approaches 5 of (x^2-3x-10)/(x^2-10x+25)

x \to 5 lim (\frac{x ^{2} - 3 x - 10}{x ^{2} - 10 x + 25})

derivative 6x^2

d er i v a t i v e 6 x^{2}

derivative of (sqrt(x)+1/(\sqrt[3]{x})^2)

\frac{d}{d x} ((x + \frac{1}{3 x})^{2})

y^{^{'}} = \frac{t ^{2}}{y}