(d^2)/(dx^2)((y)(3x^2-2x+5)^4)

解答

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

\frac{d ^{2} y}{d x ^{2}} (3 x^{2} - 2 x + 5)^{4} + 48 x (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} - 16 (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} + 12 (3 x^{2} - 2 x + 5)^{2} (6 x - 2)^{2} y + 24 (3 x^{2} - 2 x + 5)^{3} y

求解步骤

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

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

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

\frac{d}{d x} (\frac{d y}{d x} (3 x^{2} - 2 x + 5)^{4} + 4 (3 x^{2} - 2 x + 5)^{3} (6 x - 2) y) = \frac{d ^{2} y}{d x ^{2}} (3 x^{2} - 2 x + 5)^{4} + 48 x (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} - 16 (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} + 12 (3 x^{2} - 2 x + 5)^{2} (6 x - 2)^{2} y + 24 (3 x^{2} - 2 x + 5)^{3} y

= \frac{d ^{2} y}{d x ^{2}} (3 x^{2} - 2 x + 5)^{4} + 48 x (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} - 16 (3 x^{2} - 2 x + 5)^{3} \frac{d y}{d x} + 12 (3 x^{2} - 2 x + 5)^{2} (6 x - 2)^{2} y + 24 (3 x^{2} - 2 x + 5)^{3} y

e x p an d \frac{9 ( 9 k + 3 n ) ^{2}}{n ^{3}}

e x p an d \frac{( d ( b - x ) ( y - x ) )}{y}

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

s im pl i f y (\frac{b}{y} + x) (\frac{b}{y} - x)

e x p an d (ux - 2 x) (u d x + x d u)