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

解

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

4 x^{3} + 6 x y^{3}

解答ステップ

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

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

\frac{\partial}{\partial x} (y^{4}) = 0

\frac{\partial}{\partial x} (3 x^{2} y^{3}) = 6 y^{3} x

= 4 x^{3} + 0 + 6 y^{3} x

簡素化

= 4 x^{3} + 6 x y^{3}