(d^2)/(dx^2)((y)(7x^3+3x+9)^3)

解答

\frac{d ^{2}}{d x ^{2}} ((y) (7 x^{3} + 3 x + 9)^{3})

6174 x^{8} \frac{d y}{d x} + 24696 x^{7} y + 6174 x^{6} \frac{d y}{d x} + 15876 x^{5} \frac{d y}{d x} + 18522 x^{5} y + 1890 x^{4} \frac{d y}{d x} + 39690 x^{4} y + 9072 x^{3} \frac{d y}{d x} + 3780 x^{3} y + 10368 x^{2} \frac{d y}{d x} + 13608 x^{2} y + 972 x \frac{d y}{d x} + 10368 x y + (7 x^{3} + 3 x + 9)^{3} \frac{d ^{2} y}{d x ^{2}} + 1458 \frac{d y}{d x} + 486 y

求解步骤

\frac{d ^{2}}{d x ^{2}} ((y) (7 x^{3} + 3 x + 9)^{3})

\frac{d}{d x} (y (7 x^{3} + 3 x + 9)^{3}) = \frac{d y}{d x} (7 x^{3} + 3 x + 9)^{3} + 3 (7 x^{3} + 3 x + 9)^{2} (21 x^{2} + 3) y

= \frac{d}{d x} (\frac{d y}{d x} (7 x^{3} + 3 x + 9)^{3} + 3 (7 x^{3} + 3 x + 9)^{2} (21 x^{2} + 3) y)

\frac{d}{d x} (\frac{d y}{d x} (7 x^{3} + 3 x + 9)^{3} + 3 (7 x^{3} + 3 x + 9)^{2} (21 x^{2} + 3) y) = 6174 x^{8} \frac{d y}{d x} + 24696 x^{7} y + 6174 x^{6} \frac{d y}{d x} + 15876 x^{5} \frac{d y}{d x} + 18522 x^{5} y + 1890 x^{4} \frac{d y}{d x} + 39690 x^{4} y + 9072 x^{3} \frac{d y}{d x} + 3780 x^{3} y + 10368 x^{2} \frac{d y}{d x} + 13608 x^{2} y + 972 x \frac{d y}{d x} + 10368 x y + (7 x^{3} + 3 x + 9)^{3} \frac{d ^{2} y}{d x ^{2}} + 1458 \frac{d y}{d x} + 486 y

= 6174 x^{8} \frac{d y}{d x} + 24696 x^{7} y + 6174 x^{6} \frac{d y}{d x} + 15876 x^{5} \frac{d y}{d x} + 18522 x^{5} y + 1890 x^{4} \frac{d y}{d x} + 39690 x^{4} y + 9072 x^{3} \frac{d y}{d x} + 3780 x^{3} y + 10368 x^{2} \frac{d y}{d x} + 13608 x^{2} y + 972 x \frac{d y}{d x} + 10368 x y + (7 x^{3} + 3 x + 9)^{3} \frac{d ^{2} y}{d x ^{2}} + 1458 \frac{d y}{d x} + 486 y

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