(d^2)/(dx^2)((y)(3x^2+5e^x))

Lösung

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

\frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

Schritte zur Lösung

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

\frac{d}{d x} (y (3 x^{2} + 5 e^{x})) = \frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y

= \frac{d}{d x} (\frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y)

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} + 5 e^{x}) + (6 x + 5 e^{x}) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

= \frac{d ^{2} y}{d x ^{2}} (3 x^{2} + 5 e^{x}) + 2 \frac{d y}{d x} (6 x + 5 e^{x}) + (6 + 5 e^{x}) y

e x p an d lo g_{9} (\frac{z ^{5}}{x m ^{5}})

e x p an d 3 (n (n + 1))

e x p an d \frac{( w + 4 ) ( y )}{2}

e x p an d sin (x) (4 (cos (2 x))^{2} + 2 cos (x) - 1)

\frac{d}{d t} ((x) (3 x + 2 y + 4 z))