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Beliebt Rechnen >

(\partial)/(\partial x)(x^2y+xsin(y))

Lösung

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

Lösung

2 y x + sin (y)

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

\frac{\partial}{\partial x} (x sin (y)) = sin (y)

= 2 y x + sin (y)

Beliebte Beispiele

derivative f(x)=7x^4cot(x)

d er i v a t i v e f (x) = 7 x^{4} cot (x)

(\partial)/(\partial z)(-xz)

\frac{\partial}{\partial z} (- x z)

integral from 1 to 8 of (sqrt(x^2-1))/x

\int_{1}^{8} \frac{x ^{2} - 1}{x} d x

derivative of y-x

\frac{d}{d x} (y - x)

integral from 0 to pi of x*sin(nx)

\int_{0}^{π} x \cdot sin (n x) d x