derivative of (x^3-2tan(x))

解

\frac{d}{d x} ((x^{3} - 2) tan (x))

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

解答ステップ

\frac{d}{d x} ((x^{3} - 2) tan (x))

積の法則を適用:

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

f = x^{3} - 2, g = tan (x)

= \frac{d}{d x} (x^{3} - 2) tan (x) + \frac{d}{d x} (tan (x)) (x^{3} - 2)

\frac{d}{d x} (x^{3} - 2) = 3 x^{2}

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

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