(\partial)/(\partial x)((x+y)^5+(x-y)^5)

解

\frac{\partial}{\partial x} ((x + y)^{5} + (x - y)^{5})

10 x^{4} + 60 y^{2} x^{2} + 10 y^{4}

解答ステップ

\frac{\partial}{\partial x} ((x + y)^{5} + (x - y)^{5})

簡素化

(x + y)^{5} + (x - y)^{5} : 2 x^{5} + 20 x^{3} y^{2} + 10 x y^{4}

= \frac{\partial}{\partial x} (2 x^{5} + 20 x^{3} y^{2} + 10 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} (2 x^{5}) + \frac{\partial}{\partial x} (20 x^{3} y^{2}) + \frac{\partial}{\partial x} (10 x y^{4})

\frac{\partial}{\partial x} (2 x^{5}) = 10 x^{4}

\frac{\partial}{\partial x} (20 x^{3} y^{2}) = 60 y^{2} x^{2}

\frac{\partial}{\partial x} (10 x y^{4}) = 10 y^{4}

= 10 x^{4} + 60 y^{2} x^{2} + 10 y^{4}