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

Lösung

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

\frac{d ^{2} y}{d x ^{2}} (x^{3} - 3 x^{2} + 3 x) + 2 \frac{d y}{d x} (3 x^{2} - 6 x + 3) + (6 x - 6) y

Schritte zur Lösung

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

\frac{d}{d x} (y (x^{3} - 3 x^{2} + 3 x)) = \frac{d y}{d x} (x^{3} - 3 x^{2} + 3 x) + (3 x^{2} - 6 x + 3) y

= \frac{d}{d x} (\frac{d y}{d x} (x^{3} - 3 x^{2} + 3 x) + (3 x^{2} - 6 x + 3) y)

\frac{d}{d x} (\frac{d y}{d x} (x^{3} - 3 x^{2} + 3 x) + (3 x^{2} - 6 x + 3) y) = \frac{d ^{2} y}{d x ^{2}} (x^{3} - 3 x^{2} + 3 x) + 2 \frac{d y}{d x} (3 x^{2} - 6 x + 3) + (6 x - 6) y

= \frac{d ^{2} y}{d x ^{2}} (x^{3} - 3 x^{2} + 3 x) + 2 \frac{d y}{d x} (3 x^{2} - 6 x + 3) + (6 x - 6) y

e x p an d f (1, - 2) 9 x^{2} y - 4 x y^{2}

e x p an d x^{2} + y^{2} + (z - 1)^{2}

e x p an d x (2, 3, 0, - 1) + y (- 5, 4, 3, 2) + z (1, - 2, 2, 5)

\frac{d}{d h} ((V (h)) ((3 h^{2} + 4)^{\frac{3}{2}} - 8))

e x p an d \frac{5 ( 9 + 201 )}{3}