展开 (d^2y)/(d^2x)(x^3+y^3=1)

解答

展开

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

x^{2} y + \frac{y ^{4}}{x} = 1

求解步骤

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

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

使用分配律:

a (b + c) = ab + a c

a = \frac{d ^{2} y}{d ^{2} x}, b = x^{3}, c = y^{3} = 1

\frac{d ^{2} y}{d ^{2} x} x^{3} + \frac{d ^{2} y}{d ^{2} x} y^{3} = 1

乘开

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

x^{2} y + \frac{y ^{4}}{x} = 1

e x p an d (6 + 2 cos (x))^{2}

s im pl i f y (x + 4 - 3) (x + 4 + 3)

e x p an d \frac{L}{2 π} - \frac{( 4 - L ) ( 3 )}{18}

e x p an d lo g_{10} (5 3 x)

im pl i c i t \frac{d y}{d x}, 6 x y + x^{2} - 2 y^{2} = 3