derivative 3x-2y=log_{10}(3x+2y)

解答

导数

3 x - 2 y = lo g_{10} (3 x + 2 y)

\frac{d y}{d x} = - \frac{3 - 9 ln ( 10 ) x - 6 ln ( 10 ) y}{2 ( 1 + 2 ln ( 10 ) y + 3 ln ( 10 ) x )}

求解步骤

3 x - 2 y = lo g_{10} (3 x + 2 y)

将

y

视为

y (x)

对两侧微分:

3 - 2 \frac{d y}{d x} = \frac{3 + 2 \frac{d y}{d x}}{ln ( 10 ) ( 3 x + 2 y )}

整理

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{3 - 9 ln ( 10 ) x - 6 ln ( 10 ) y}{2 ( 1 + 2 ln ( 10 ) y + 3 ln ( 10 ) x )}

\frac{d y}{d x} = - \frac{3 - 9 ln ( 10 ) x - 6 ln ( 10 ) y}{2 ( 1 + 2 ln ( 10 ) y + 3 ln ( 10 ) x )}

d er i v a t i v e x^{2} + 5 y^{2} = 5

d er i v a t i v e 3 + sin (y) = y - x^{3}

d er i v a t i v e x^{2} + 2 x y = 3 y^{2}

d er i v a t i v e 2 x y - 4 y + 5 = 0

d er i v a t i v e x^{4} + y^{4} = 4 a^{2} x^{3} y^{3}