(\partial)/(\partial y)(sin^4(1-4xy+y^2))

Lösung

\frac{\partial}{\partial y} (sin^{4} (1 - 4 x y + y^{2}))

4 sin^{3} (1 - 4 x y + y^{2}) cos (1 - 4 x y + y^{2}) (2 y - 4 x)

Schritte zur Lösung

\frac{\partial}{\partial y} (sin^{4} (1 - 4 x y + y^{2}))

Behandle

x

als Konstante

Wende die Kettenregel an:

4 (sin (1 - 4 x y + y^{2}))^{3} \frac{\partial}{\partial y} (sin (1 - 4 x y + y^{2}))

= 4 (sin (1 - 4 x y + y^{2}))^{3} \frac{\partial}{\partial y} (sin (1 - 4 x y + y^{2}))

\frac{\partial}{\partial y} (sin (1 - 4 x y + y^{2})) = cos (1 - 4 x y + y^{2}) (2 y - 4 x)

= 4 (sin (1 - 4 x y + y^{2}))^{3} cos (1 - 4 x y + y^{2}) (2 y - 4 x)

Vereinfache

= 4 sin^{3} (1 - 4 x y + y^{2}) cos (1 - 4 x y + y^{2}) (2 y - 4 x)

d er i v a t i v e f (x) = 500 - y - \frac{4 y}{y + 3}

\int \frac{1}{4 x ^{2} + 5} d x

x \to 0 lim (cos (π) x)

\int 3 x^{- \frac{2}{3}} d x

\int e^{2 x} (sin (3 x)) d x