斜率 eln(2x^4+ax^2y^{2+2y^4})

解答

斜率

e ln (2 x^{4} + a x^{2} y^{2 + 2 y^{4}})

\frac{8 e x ^{2} + 2 e a y ^{2 y^{4} + 2}}{x ( 2 x ^{2} + a y ^{2 (y^{4} + 1)} - 2 e a y ^{1 + 2 y^{4}} - 2 e a y ^{5 + 2 y^{4}} - 8 e a y ^{5 + 2 y^{4}} ln ( y ) )}

求解步骤

y = e ln (2 x^{4} + a x^{2} y^{2 + 2 y^{4}})

使用隐函数微分确定

y = e ln (2 x^{4} + a x^{2} y^{2 + 2 y^{4}})

的斜率

隐函数

y = e ln (2 x^{4} + a x^{2} y^{2 + 2 y^{4}})

的导数:

\frac{8 e x ^{2} + 2 e a y ^{2 y^{4} + 2}}{x ( 2 x ^{2} + a y ^{2 (y^{4} + 1)} - 2 e a y ^{1 + 2 y^{4}} - 2 e a y ^{5 + 2 y^{4}} - 8 e a y ^{5 + 2 y^{4}} ln ( y ) )}

\frac{8 e x ^{2} + 2 e a y ^{2 y^{4} + 2}}{x ( 2 x ^{2} + a y ^{2 (y^{4} + 1)} - 2 e a y ^{1 + 2 y^{4}} - 2 e a y ^{5 + 2 y^{4}} - 8 e a y ^{5 + 2 y^{4}} ln ( y ) )}

d er i v a t i v e (8 x^{2} - x) ln (x)

n = 0 \sum \infty (\frac{- 1}{3})^{2 n}

\int \frac{23}{x ^{3} - 125} d x

d er i v a t i v e h (x) = \frac{3}{x ^{2}} + \frac{5}{x ^{4}}

x y^{^{'}} - 2 y = 7 x^{2}