(d^2)/(dx^2)((y)(e^{3x}-kx))

Lösung

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

\frac{d ^{2} y}{d x ^{2}} (e^{3 x} - k x) + 2 \frac{d y}{d x} (3 e^{3 x} - k) + 9 e^{3 x} y

Schritte zur Lösung

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

\frac{d}{d x} (y (e^{3 x} - k x)) = \frac{d y}{d x} (e^{3 x} - k x) + (e^{3 x} \cdot 3 - k) y

= \frac{d}{d x} (\frac{d y}{d x} (e^{3 x} - k x) + (e^{3 x} \cdot 3 - k) y)

\frac{d}{d x} (\frac{d y}{d x} (e^{3 x} - k x) + (e^{3 x} \cdot 3 - k) y) = \frac{d ^{2} y}{d x ^{2}} (e^{3 x} - k x) + 2 \frac{d y}{d x} (3 e^{3 x} - k) + 9 e^{3 x} y

= \frac{d ^{2} y}{d x ^{2}} (e^{3 x} - k x) + 2 \frac{d y}{d x} (3 e^{3 x} - k) + 9 e^{3 x} y

e x p an d \frac{π ( 1 + 2 )}{2}

e x p an d \frac{1}{( s - 1 ) ( s + 2 )}

e x p an d (x^{2} - 3 y^{2} = 7,) - (x^{2} + y = 9)

e x p an d (4 y - t^{2}, (4 - t)^{2}) \cdot (- 1, 4 - 2 t)

s im pl i f y (x - i)^{3}