(d^2}{dx^2}((y)(\frac{4x^5)/5-7x))

Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (\frac{4 x ^{5}}{5} - 7 x))

\frac{d ^{2} y}{d x ^{2}} (\frac{4 x ^{5}}{5} - 7 x) + 2 \frac{d y}{d x} (4 x^{4} - 7) + 16 x^{3} y

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} ((y) (\frac{4 x ^{5}}{5} - 7 x))

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

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

\frac{d}{d x} (\frac{d y}{d x} (\frac{4 x ^{5}}{5} - 7 x) + (4 x^{4} - 7) y) = \frac{d ^{2} y}{d x ^{2}} (\frac{4 x ^{5}}{5} - 7 x) + 2 \frac{d y}{d x} (4 x^{4} - 7) + 16 x^{3} y

= \frac{d ^{2} y}{d x ^{2}} (\frac{4 x ^{5}}{5} - 7 x) + 2 \frac{d y}{d x} (4 x^{4} - 7) + 16 x^{3} y

e x p an d 4 \cdot (t - 1) \cdot e^{- 0.5 \cdot t} + 8

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

e x p an d \frac{6 x ( y - 1 ) ^{3}}{2 x ^{2} + ( y - 1 ) ^{6}}

e x p an d \frac{( x ^{3} + k x ^{2} - ( k + 5 ) x - 19 )}{( x + 3 )}

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