(d^2)/(dx^2)((y)(5x^2-3)(7x^3+x))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (5 x^{2} - 3) (7 x^{3} + x))

\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 3) (7 x^{3} + x) + 2 \frac{d y}{d x} (175 x^{4} - 48 x^{2} - 3) + (700 x^{3} - 96 x) y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (5 x^{2} - 3) (7 x^{3} + x))

\frac{d}{d x} (y (5 x^{2} - 3) (7 x^{3} + x)) = \frac{d y}{d x} (5 x^{2} - 3) (7 x^{3} + x) + (175 x^{4} - 48 x^{2} - 3) y

= \frac{d}{d x} (\frac{d y}{d x} (5 x^{2} - 3) (7 x^{3} + x) + (175 x^{4} - 48 x^{2} - 3) y)

\frac{d}{d x} (\frac{d y}{d x} (5 x^{2} - 3) (7 x^{3} + x) + (175 x^{4} - 48 x^{2} - 3) y) = \frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 3) (7 x^{3} + x) + 2 \frac{d y}{d x} (175 x^{4} - 48 x^{2} - 3) + (700 x^{3} - 96 x) y

= \frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 3) (7 x^{3} + x) + 2 \frac{d y}{d x} (175 x^{4} - 48 x^{2} - 3) + (700 x^{3} - 96 x) y

s im pl i f y (x - 4 + 1)^{2}

e x p an d \frac{4 ( 20 10 - 2 )}{27}

e x p an d \frac{8 ( 12 - 24 c )}{35}

\frac{d}{d y} ((x (y)) (y^{4} + 4))

e x p an d (v cos (o) t + x)^{2} + (v sin (o) t + y)^{2}