(\partial)/(\partial x)(sin(5x^4y-3xy^4))

Lösung

\frac{\partial}{\partial x} (sin (5 x^{4} y - 3 x y^{4}))

cos (5 x^{4} y - 3 x y^{4}) (20 y x^{3} - 3 y^{4})

Schritte zur Lösung

\frac{\partial}{\partial x} (sin (5 x^{4} y - 3 x y^{4}))

Behandle

y

als Konstante

Wende die Kettenregel an:

cos (5 x^{4} y - 3 x y^{4}) \frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4})

= cos (5 x^{4} y - 3 x y^{4}) \frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4})

\frac{\partial}{\partial x} (5 x^{4} y - 3 x y^{4}) = 20 y x^{3} - 3 y^{4}

= cos (5 x^{4} y - 3 x y^{4}) (20 y x^{3} - 3 y^{4})

\frac{\partial}{\partial y} ((x^{2} + x y)^{3})

3 y^{^{'}} - 2 y = e^{- \frac{π t}{2}}

d er i v a t i v e 6 x^{5} e^{x} + e^{x} x^{6}

n = 1 \sum \infty \frac{4}{n ( n + 2 )}

y^{^{''}} - 4 y^{^{'}} - 5 y = 9 e^{2 t}