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

Lösung

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

\frac{d ^{2} y}{d x ^{2}} (5 x^{3} + sin (x)) + 2 \frac{d y}{d x} (15 x^{2} + cos (x)) + (30 x - sin (x)) y

Schritte zur Lösung

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

\frac{d}{d x} (y (5 x^{3} + sin (x))) = \frac{d y}{d x} (5 x^{3} + sin (x)) + (15 x^{2} + cos (x)) y

= \frac{d}{d x} (\frac{d y}{d x} (5 x^{3} + sin (x)) + (15 x^{2} + cos (x)) y)

\frac{d}{d x} (\frac{d y}{d x} (5 x^{3} + sin (x)) + (15 x^{2} + cos (x)) y) = \frac{d ^{2} y}{d x ^{2}} (5 x^{3} + sin (x)) + 2 \frac{d y}{d x} (15 x^{2} + cos (x)) + (30 x - sin (x)) y

= \frac{d ^{2} y}{d x ^{2}} (5 x^{3} + sin (x)) + 2 \frac{d y}{d x} (15 x^{2} + cos (x)) + (30 x - sin (x)) y

e x p an d ((- 1.1, 3.7) + (- 5, 1.5)) (- 2.9)

e x p an d (9 x - 2 y = 11) (5)

e x p an d (x + y) (x - y) d x

e x p an d \frac{x ^{2} - 16 + 6 a x + 24 a}{6 ( x + 4 )}

e x p an d \frac{45 ( y - 3 ) ^{2}}{2}