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Beliebt Rechnen >

(\partial)/(\partial y)(xsin(y-x))

Lösung

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

Lösung

x cos (y - x)

Schritte zur Lösung

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

Behandle

x

als Konstante

Entferne die Konstante:

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

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

Wende die Kettenregel an:

cos (y - x) \frac{\partial}{\partial y} (y - x)

= cos (y - x) \frac{\partial}{\partial y} (y - x)

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

= x cos (y - x) \cdot 1

Vereinfache

= x cos (y - x)

Beliebte Beispiele

derivative of xy+y-1

\frac{d}{d x} (x y + y - 1)

integral from 4 to 5 of 1/((x-4)^{4/3)}

\int_{4}^{5} \frac{1}{( x - 4 ) ^{\frac{4}{3}}} d x

derivative f(x)=e^{x+2}+1

d er i v a t i v e f (x) = e^{x + 2} + 1

derivative of (x^2-2/(x-1))

\frac{d}{d x} (\frac{x ^{2} - 2}{x - 1})

limit as x approaches 0 of ln|x|

x \to 0 lim (ln ∣ x ∣)