derivative x^4+y^4=4a^2x^3y^3

解答

导数

x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}

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

求解步骤

x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}

将

y

视为

y (x)

对两侧微分:

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

整理

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

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

d er i v a t i v e x^{4} + y^{4} = x^{2} y^{2}

d er i v a t i v e s = \frac{1}{t}

d er i v a t i v e x^{2} + y^{2} x + 6 x = 1

d er i v a t i v e x = \frac{y ^{3}}{3 + y}

d er i v a t i v e x^{2} + y^{2} = 2 x y