derivative of y^2=2ax

解答

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

y = a x^{2} + c_{1}, y = - a x^{2} + c_{1}

求解步骤

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

若

f^{^{'}} (x) = g (x)

则

f (x) = \int g (x) d x

y^{2} = \int 2 a x d x

\int 2 a x d x = a x^{2} + c_{1}

y^{2} = a x^{2} + c_{1}

整理

y : y = a x^{2} + c_{1}, y = - a x^{2} + c_{1}

y = a x^{2} + c_{1}, y = - a x^{2} + c_{1}

\frac{d v}{d t} = 9 - \frac{3 v}{2}

y^{^{'}} - 7 x y^{2} = 3 x

d x - 11 x y d y = 2 y d y

\frac{y - x y ^{^{'}}}{y ^{2}} + \frac{x y ^{^{'}} - y}{x ^{2}} = 0

- 2 x - 9 y^{2} \frac{d y}{d x} = 0