(d^2)/(dx^2)((y)(4x^7-5x^2+x))

Lösung

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

\frac{d ^{2} y}{d x ^{2}} (4 x^{7} - 5 x^{2} + x) + 2 \frac{d y}{d x} (28 x^{6} - 10 x + 1) + (168 x^{5} - 10) y

Schritte zur Lösung

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

\frac{d}{d x} (y (4 x^{7} - 5 x^{2} + x)) = \frac{d y}{d x} (4 x^{7} - 5 x^{2} + x) + (28 x^{6} - 10 x + 1) y

= \frac{d}{d x} (\frac{d y}{d x} (4 x^{7} - 5 x^{2} + x) + (28 x^{6} - 10 x + 1) y)

\frac{d}{d x} (\frac{d y}{d x} (4 x^{7} - 5 x^{2} + x) + (28 x^{6} - 10 x + 1) y) = \frac{d ^{2} y}{d x ^{2}} (4 x^{7} - 5 x^{2} + x) + 2 \frac{d y}{d x} (28 x^{6} - 10 x + 1) + (168 x^{5} - 10) y

= \frac{d ^{2} y}{d x ^{2}} (4 x^{7} - 5 x^{2} + x) + 2 \frac{d y}{d x} (28 x^{6} - 10 x + 1) + (168 x^{5} - 10) y

e x p an d \frac{cos ( x + h ) - cos ( x )}{h}

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

e x p an d \frac{( x + 1 ) ( x ^{4} + x ^{3} + x ^{2} + x )}{x - 1}

e x p an d V (- 6, - 3) F (- 4, - 3)

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