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Beliebt Rechnen >

(\partial)/(\partial x)(x*Y(x))

Lösung

\frac{\partial}{\partial x} (x \cdot Y (x))

Lösung

Y (x) + x \frac{\partial}{\partial x} (Y (x))

Schritte zur Lösung

\frac{\partial}{\partial x} (x Y (x))

Wende die Produktregel an:

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

f = x, g = Y (x)

= \frac{\partial}{\partial x} (x) Y (x) + \frac{\partial}{\partial x} (Y (x)) x

\frac{\partial}{\partial x} (x) = 1

= 1 \cdot Y (x) + \frac{\partial}{\partial x} (Y (x)) x

Vereinfache

= Y (x) + x \frac{\partial}{\partial x} (Y (x))

Beliebte Beispiele

fläche 5-x^2,sin(x),-2.385,2.025

a re a 5 - x^{2}, sin (x), - 2.385, 2.025

derivative (4-x^2)^5

d er i v a t i v e (4 - x^{2})^{5}

integral of (e^x+1/(3x))

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

derivative (2/5 x)^9

d er i v a t i v e (\frac{2}{5} x)^{9}

integral from 0 to pi/4 of 2sec(t)

\int_{0}^{\frac{π}{4}} 2 sec (t) d t