(d^2)/(dx^2)((y)(x^2-1)^3)

解答

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 1)^{3})

\frac{d ^{2} y}{d x ^{2}} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} \frac{d y}{d x} + 6 (x^{5} \frac{d y}{d x} + 5 x^{4} y - 2 x^{3} \frac{d y}{d x} - 6 x^{2} y + x \frac{d y}{d x} + y)

求解步骤

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 1)^{3})

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

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

\frac{d}{d x} (\frac{d y}{d x} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} y) = \frac{d ^{2} y}{d x ^{2}} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} \frac{d y}{d x} + 6 (x^{5} \frac{d y}{d x} + 5 x^{4} y - 2 x^{3} \frac{d y}{d x} - 6 x^{2} y + x \frac{d y}{d x} + y)

= \frac{d ^{2} y}{d x ^{2}} (x^{2} - 1)^{3} + 6 x (x^{2} - 1)^{2} \frac{d y}{d x} + 6 (x^{5} \frac{d y}{d x} + 5 x^{4} y - 2 x^{3} \frac{d y}{d x} - 6 x^{2} y + x \frac{d y}{d x} + y)

e x p an d (e^{2 x}) (\frac{x}{4} + A) + (e^{- 2 x}) (\frac{1}{16} e^{4 x} + B)

\frac{d ^{2}}{d x ^{2}} ((y) ((a \cdot x) + ((1 - a) \cdot x^{2})))

\frac{\partial}{\partial v} ((x) (9 u + 2 v))

e x p an d (x - 2) \cdot x \cdot (72 + 7 x)

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