derivative of y^2=x+1

解

\frac{d}{d x} (y^{2}) = x + 1

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

解答ステップ

\frac{d}{d x} (y^{2}) = x + 1

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

であれば

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

y^{2} = \int x + 1 d x

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

y^{2} = \frac{x ^{2}}{2} + x + c_{1}

分離する

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

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