(\partial)/(\partial x)(x^2tan(4x^4y))

解

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

2 x tan (4 x^{4} y) + 16 x^{5} y sec^{2} (4 x^{4} y)

解答ステップ

\frac{\partial}{\partial x} (x^{2} tan (4 x^{4} 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^{2}, g = tan (4 x^{4} y)

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

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

\frac{\partial}{\partial x} (tan (4 x^{4} y)) = sec^{2} (4 x^{4} y) \cdot 16 y x^{3}

= 2 x tan (4 x^{4} y) + sec^{2} (4 x^{4} y) \cdot 16 y x^{3} x^{2}

sec^{2} (4 x^{4} y) \cdot 16 y x^{3} x^{2} = 16 x^{5} y sec^{2} (4 x^{4} y)

= 2 x tan (4 x^{4} y) + 16 x^{5} y sec^{2} (4 x^{4} y)