derivative of x^2sec(y)=8x

解

\frac{d}{d x} (x^{2} sec (y)) = 8 x

y = arcsec (\frac{4 x ^{2} + c _{1}}{x ^{2}}) + 2 πn, y = - arcsec (\frac{4 x ^{2} + c _{1}}{x ^{2}}) + 2 πn

解答ステップ

\frac{d}{d x} (x^{2} sec (y)) = 8 x

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

であれば

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

x^{2} sec (y) = \int 8 x d x

\int 8 x d x = 4 x^{2} + c_{1}

x^{2} sec (y) = 4 x^{2} + c_{1}

分離する

y : y = arcsec (\frac{4 x ^{2} + c _{1}}{x ^{2}}) + 2 πn, y = - arcsec (\frac{4 x ^{2} + c _{1}}{x ^{2}}) + 2 πn

y = arcsec (\frac{4 x ^{2} + c _{1}}{x ^{2}}) + 2 πn, y = - arcsec (\frac{4 x ^{2} + c _{1}}{x ^{2}}) + 2 πn