(d^2)/(dx^2)((y)(5x-6)^2)

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (5 x - 6)^{2})

25 x^{2} \frac{d ^{2} y}{d x ^{2}} - 60 x \frac{d ^{2} y}{d x ^{2}} + 100 x \frac{d y}{d x} + 36 \frac{d ^{2} y}{d x ^{2}} - 120 \frac{d y}{d x} + 50 y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (5 x - 6)^{2})

\frac{d}{d x} (y (5 x - 6)^{2}) = \frac{d y}{d x} (5 x - 6)^{2} + 10 (5 x - 6) y

= \frac{d}{d x} (\frac{d y}{d x} (5 x - 6)^{2} + 10 (5 x - 6) y)

\frac{d}{d x} (\frac{d y}{d x} (5 x - 6)^{2} + 10 (5 x - 6) y) = 25 x^{2} \frac{d ^{2} y}{d x ^{2}} - 60 x \frac{d ^{2} y}{d x ^{2}} + 100 x \frac{d y}{d x} + 36 \frac{d ^{2} y}{d x ^{2}} - 120 \frac{d y}{d x} + 50 y

= 25 x^{2} \frac{d ^{2} y}{d x ^{2}} - 60 x \frac{d ^{2} y}{d x ^{2}} + 100 x \frac{d y}{d x} + 36 \frac{d ^{2} y}{d x ^{2}} - 120 \frac{d y}{d x} + 50 y

s im pl i f y (5 x - 2)^{2}

s im pl i f y (3 x + 9 x^{2} - 6 x + 3) (3 x - 9 x^{2} - 6 x + 3)

e x p an d (2 v x^{2} + x^{2} + 3 v^{2} x^{2}) (v d x + x d v)

e x p an d 4 (- 4 e^{x^{2} - y^{2}} x^{2} y - 2 e^{x^{2} - y^{2}} y)

e x p an d (x + x^{2} + 1)^{10}