(d^2)/(dx^2)((y)(y^3-xy))

解答

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

- 2 x \frac{d y}{d x}^{2} - 2 x y \frac{d ^{2} y}{d x ^{2}} - 4 y \frac{d y}{d x} + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

求解步骤

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

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

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

\frac{d}{d x} (- 2 x y \frac{d y}{d x} + 4 y^{3} \frac{d y}{d x} - y^{2}) = - 2 x \frac{d y}{d x}^{2} - 2 x y \frac{d ^{2} y}{d x ^{2}} - 4 y \frac{d y}{d x} + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

= - 2 x \frac{d y}{d x}^{2} - 2 x y \frac{d ^{2} y}{d x ^{2}} - 4 y \frac{d y}{d x} + 12 y^{2} \frac{d y}{d x}^{2} + 4 y^{3} \frac{d ^{2} y}{d x ^{2}}

s im pl i f y (35 y - 4)^{2}

e x p an d se x (csc (x) + sin (x)) + cos (x) (sec (x) + cos (x)) + 1

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

e x p an d - \frac{144 ( - x ^{2} + 4 )}{( x ^{2} + 12 ) ^{3}}

e x p an d x \cdot (x + 1)