(\partial)/(\partial x)(x^3sec^2(xy))

解

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

3 x^{2} sec^{2} (x y) + 2 y sec^{2} (y x) tan (y x) x^{3}

解答ステップ

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

y

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = sec^{2} (x y)

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

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

\frac{\partial}{\partial x} (sec^{2} (x y)) = 2 y sec^{2} (y x) tan (y x)

= 3 x^{2} sec^{2} (x y) + 2 y sec^{2} (y x) tan (y x) x^{3}