(d^2)/(dx^2)((y)(4cos(3x)+6sin(3x)))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (4 cos (3 x) + 6 sin (3 x)))

\frac{d ^{2} y}{d x ^{2}} (4 cos (3 x) + 6 sin (3 x)) + 2 \frac{d y}{d x} (- 12 sin (3 x) + 18 cos (3 x)) + (- 36 cos (3 x) - 54 sin (3 x)) y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (4 cos (3 x) + 6 sin (3 x)))

\frac{d}{d x} (y (4 cos (3 x) + 6 sin (3 x))) = \frac{d y}{d x} (4 cos (3 x) + 6 sin (3 x)) + (- 12 sin (3 x) + 18 cos (3 x)) y

= \frac{d}{d x} (\frac{d y}{d x} (4 cos (3 x) + 6 sin (3 x)) + (- 12 sin (3 x) + 18 cos (3 x)) y)

\frac{d}{d x} (\frac{d y}{d x} (4 cos (3 x) + 6 sin (3 x)) + (- 12 sin (3 x) + 18 cos (3 x)) y) = \frac{d ^{2} y}{d x ^{2}} (4 cos (3 x) + 6 sin (3 x)) + 2 \frac{d y}{d x} (- 12 sin (3 x) + 18 cos (3 x)) + (- 36 cos (3 x) - 54 sin (3 x)) y

= \frac{d ^{2} y}{d x ^{2}} (4 cos (3 x) + 6 sin (3 x)) + 2 \frac{d y}{d x} (- 12 sin (3 x) + 18 cos (3 x)) + (- 36 cos (3 x) - 54 sin (3 x)) y

e x p an d \frac{d}{d x} ((7 x^{2} - 5) e^{x}) - 5 x^{2}

e x p an d \frac{2 ( 30 x ^{2} + 9 x - 20 )}{( 2 x + 1 ) ( 3 x ^{2} - 5 )}

e x p an d f (x) ((x) = 4 x - 6)

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

e x p an d \frac{( 1 + x ^{- 1} ) ^{3}}{- 3}