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Beliebt Rechnen >

(\partial)/(\partial x)(sin(xye^{x^2}))

Lösung

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

Lösung

cos (x y e^{x^{2}}) y (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

= cos (x y e^{x^{2}}) y (e^{x^{2}} + 2 e^{x^{2}} x^{2})

Beliebte Beispiele

f^'(x)=2^{4x}+4x^2

integral of (1-2x)^9

derivative e^t*cos(2t)

integral of ((2x)/(1+x^2))

integral of ((x+1))/(x^2(x-1))