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Beliebt Rechnen >

(\partial)/(\partial x)(4ysin(x^2y))

Lösung

\frac{\partial}{\partial x} (4 y sin (x^{2} y))

Lösung

8 y^{2} x cos (y x^{2})

Schritte zur Lösung

\frac{\partial}{\partial x} (4 y sin (x^{2} y))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 4 y \frac{\partial}{\partial x} (sin (x^{2} y))

Wende die Kettenregel an:

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

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

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

= 4 y cos (x^{2} y) \cdot 2 y x

Vereinfache

4 y cos (x^{2} y) \cdot 2 y x : 8 y^{2} x cos (y x^{2})

= 8 y^{2} x cos (y x^{2})

Beliebte Beispiele

integral from 0 to pi/2 of sin^3(t)

\int_{0}^{\frac{π}{2}} sin^{3} (t) d t

derivative of (3x^2-2/(2x+3))

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

integral from 0 to 8 of 2pix(x^{3/2})

\int_{0}^{8} 2 π x (x^{\frac{3}{2}}) d x

integral of 8xsec^2(x)

\int 8 x sec^{2} (x) d x

integral of xsin(2ax)

\int x sin (2 a x) d x