(\partial}{\partial x}(4e^{\frac{x^2)/y}-cos(xy^3))

解

\frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}} - cos (x y^{3}))

\frac{8 e ^{\frac{x ^{2}}{y}} x}{y} + y^{3} sin (x y^{3})

解答ステップ

\frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}} - cos (x y^{3}))

y

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}}) - \frac{\partial}{\partial x} (cos (x y^{3}))

\frac{\partial}{\partial x} (4 e^{\frac{x ^{2}}{y}}) = \frac{8 e ^{\frac{x ^{2}}{y}} x}{y}

\frac{\partial}{\partial x} (cos (x y^{3})) = - sin (x y^{3}) y^{3}

= \frac{8 e ^{\frac{x ^{2}}{y}} x}{y} - (- sin (x y^{3}) y^{3})

簡素化

= \frac{8 e ^{\frac{x ^{2}}{y}} x}{y} + y^{3} sin (x y^{3})