derivative of y^3=50x

解

\frac{d}{d x} (y^{3}) = 50 x

y = 3 25 x^{2} + c_{1}, y = - \frac{3 25 x ^{2} + c _{1}}{2} + \frac{3 25 x ^{2} + c _{1} 3}{2} i, y = - \frac{3 25 x ^{2} + c _{1}}{2} - \frac{3 25 x ^{2} + c _{1} 3}{2} i

解答ステップ

\frac{d}{d x} (y^{3}) = 50 x

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

であれば

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

y^{3} = \int 50 x d x

\int 50 x d x = 25 x^{2} + c_{1}

y^{3} = 25 x^{2} + c_{1}

分離する

y : y = 3 25 x^{2} + c_{1}, y = - \frac{3 25 x ^{2} + c _{1}}{2} + \frac{3 25 x ^{2} + c _{1} 3}{2} i, y = - \frac{3 25 x ^{2} + c _{1}}{2} - \frac{3 25 x ^{2} + c _{1} 3}{2} i

y = 3 25 x^{2} + c_{1}, y = - \frac{3 25 x ^{2} + c _{1}}{2} + \frac{3 25 x ^{2} + c _{1} 3}{2} i, y = - \frac{3 25 x ^{2} + c _{1}}{2} - \frac{3 25 x ^{2} + c _{1} 3}{2} i