(\partial)/(\partial x)(x^5+3x^3y^2+3xy^4)

解

\frac{\partial}{\partial x} (x^{5} + 3 x^{3} y^{2} + 3 x y^{4})

5 x^{4} + 9 y^{2} x^{2} + 3 y^{4}

解答ステップ

\frac{\partial}{\partial x} (x^{5} + 3 x^{3} y^{2} + 3 x y^{4})

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} (x^{5}) + \frac{\partial}{\partial x} (3 x^{3} y^{2}) + \frac{\partial}{\partial x} (3 x y^{4})

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

\frac{\partial}{\partial x} (3 x^{3} y^{2}) = 9 y^{2} x^{2}

\frac{\partial}{\partial x} (3 x y^{4}) = 3 y^{4}

= 5 x^{4} + 9 y^{2} x^{2} + 3 y^{4}