(d^2)/(dx^2)((y)(4x^2+9y^2))

解答

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{2} + 9 y^{2}))

4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 54 y \frac{d y}{d x}^{2} + 27 y^{2} \frac{d ^{2} y}{d x ^{2}}

求解步骤

\frac{d ^{2}}{d x ^{2}} ((y) (4 x^{2} + 9 y^{2}))

\frac{d}{d x} (y (4 x^{2} + 9 y^{2})) = 4 x^{2} \frac{d y}{d x} + 8 x y + 27 y^{2} \frac{d y}{d x}

= \frac{d}{d x} (4 x^{2} \frac{d y}{d x} + 8 x y + 27 y^{2} \frac{d y}{d x})

\frac{d}{d x} (4 x^{2} \frac{d y}{d x} + 8 x y + 27 y^{2} \frac{d y}{d x}) = 4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 54 y \frac{d y}{d x}^{2} + 27 y^{2} \frac{d ^{2} y}{d x ^{2}}

= 4 x^{2} \frac{d ^{2} y}{d x ^{2}} + 16 x \frac{d y}{d x} + 8 y + 54 y \frac{d y}{d x}^{2} + 27 y^{2} \frac{d ^{2} y}{d x ^{2}}

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

e x p an d \frac{( x - 1 ) ( x + 5 )}{( x + 1 )}

e x p an d \frac{2 x ^{3} + 17 x ^{2} - 40 x + 25}{( x + 5 ) ( 2 x + 5 )}

e x p an d \frac{( 4 x + 13 ) ^{2}}{4}

e x p an d (+ 3 - 6 + 9 = 0,) (- 4 + 7 + 2 = 0)