(d^2)/(dx^2)((y)(12)(5x^2-1)(x^2-1))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (12) (5 x^{2} - 1) (x^{2} - 1))

12 (\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 1) (x^{2} - 1) + 2 (20 x^{3} - 12 x) \frac{d y}{d x} + (60 x^{2} - 12) y)

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (12) (5 x^{2} - 1) (x^{2} - 1))

\frac{d}{d x} (y \cdot 12 (5 x^{2} - 1) (x^{2} - 1)) = 12 (\frac{d y}{d x} (5 x^{2} - 1) (x^{2} - 1) + (20 x^{3} - 12 x) y)

= \frac{d}{d x} (12 (\frac{d y}{d x} (5 x^{2} - 1) (x^{2} - 1) + (20 x^{3} - 12 x) y))

\frac{d}{d x} (12 (\frac{d y}{d x} (5 x^{2} - 1) (x^{2} - 1) + (20 x^{3} - 12 x) y)) = 12 (\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 1) (x^{2} - 1) + 2 (20 x^{3} - 12 x) \frac{d y}{d x} + (60 x^{2} - 12) y)

= 12 (\frac{d ^{2} y}{d x ^{2}} (5 x^{2} - 1) (x^{2} - 1) + 2 (20 x^{3} - 12 x) \frac{d y}{d x} + (60 x^{2} - 12) y)

e x p an d - e^{an} (e^{- x n} - e^{- an})

e x p an d \frac{s + 2}{( s + 3 ) ( s ^{2} + 2 s + 2 )}

e x p an d a \cdot (b + c + d + e) + b \cdot (c + d + e) + c \cdot (d + e) + d \cdot e

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

e x p an d \frac{x + 5}{( x + 2 ) ^{2}}