(d^2)/(dx^2)((y)((4x^2-1)^2))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) ((4 x^{2} - 1)^{2}))

16 x^{4} \frac{d ^{2} y}{d x ^{2}} + 128 x^{3} \frac{d y}{d x} - 8 x^{2} \frac{d ^{2} y}{d x ^{2}} + 192 x^{2} y - 32 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 16 y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) ((4 x^{2} - 1)^{2}))

\frac{d}{d x} (y (4 x^{2} - 1)^{2}) = \frac{d y}{d x} (4 x^{2} - 1)^{2} + 16 x (4 x^{2} - 1) y

= \frac{d}{d x} (\frac{d y}{d x} (4 x^{2} - 1)^{2} + 16 x (4 x^{2} - 1) y)

\frac{d}{d x} (\frac{d y}{d x} (4 x^{2} - 1)^{2} + 16 x (4 x^{2} - 1) y) = 16 x^{4} \frac{d ^{2} y}{d x ^{2}} + 128 x^{3} \frac{d y}{d x} - 8 x^{2} \frac{d ^{2} y}{d x ^{2}} + 192 x^{2} y - 32 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 16 y

= 16 x^{4} \frac{d ^{2} y}{d x ^{2}} + 128 x^{3} \frac{d y}{d x} - 8 x^{2} \frac{d ^{2} y}{d x ^{2}} + 192 x^{2} y - 32 x \frac{d y}{d x} + \frac{d ^{2} y}{d x ^{2}} - 16 y

e x p an d (cot (x) - tan (x)) sin^{2} (x)

e x p an d 4 π (\frac{125 - 21 21}{3} - 221)

s im pl i f y (1 - \frac{1}{x}) (1 - \frac{2}{x + 2}) (1 - \frac{3}{x + 5}) (1 - \frac{4}{x + 9})

e x p an d sin (2 (n + 1))

s im pl i f y - 6.3 (A + B sin (D x) + C cos (D x))