derivative of x^2tan(xy)

解

\frac{d}{d x} (x^{2} tan (x y))

2 x tan (x y) + sec^{2} (x y) (y + x \frac{d y}{d x}) x^{2}

解答ステップ

\frac{d}{d x} (x^{2} tan (x y))

積の法則を適用:

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

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

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

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

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

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