derivative tan^2(9x)

解答

导数

tan^{2} (9 x)

18 sec^{2} (9 x) tan (9 x)

求解步骤

\frac{d}{d x} (tan^{2} (9 x))

使用连锁律:

2 tan (9 x) \frac{d}{d x} (tan (9 x))

= 2 tan (9 x) \frac{d}{d x} (tan (9 x))

\frac{d}{d x} (tan (9 x)) = sec^{2} (9 x) \cdot 9

= 2 tan (9 x) sec^{2} (9 x) \cdot 9

化简

= 18 sec^{2} (9 x) tan (9 x)

x \to 4 lim (x^{2} - 9)

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