(d^2)/(dx^2)((y)(5-3x)^3)

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (5 - 3 x)^{3})

\frac{d ^{2} y}{d x ^{2}} (5 - 3 x)^{3} - 18 \frac{d y}{d x} (5 - 3 x)^{2} + 270 y - 162 x y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (5 - 3 x)^{3})

\frac{d}{d x} (y (5 - 3 x)^{3}) = \frac{d y}{d x} (5 - 3 x)^{3} - 9 (5 - 3 x)^{2} y

= \frac{d}{d x} (\frac{d y}{d x} (5 - 3 x)^{3} - 9 (5 - 3 x)^{2} y)

\frac{d}{d x} (\frac{d y}{d x} (5 - 3 x)^{3} - 9 (5 - 3 x)^{2} y) = \frac{d ^{2} y}{d x ^{2}} (5 - 3 x)^{3} - 18 \frac{d y}{d x} (5 - 3 x)^{2} + 270 y - 162 x y

= \frac{d ^{2} y}{d x ^{2}} (5 - 3 x)^{3} - 18 \frac{d y}{d x} (5 - 3 x)^{2} + 270 y - 162 x y

e x p an d \frac{2 λ ^{2}}{( λ + s ) ( 2 λ + s )}

e x p an d sin (cos ((x + y)^{2}))

e x p an d (y ln (y) - e^{- x y}) d x

e x p an d \frac{1}{( x ) ( x - 1 ) ( x + 6 )}

e x p an d d x (\frac{10}{z ^{2}} - \frac{4}{z ^{6}})