derivative of tan^n(x)

解答

\frac{d}{d x} (tan^{n} (x))

n sec^{2} (x) tan^{n - 1} (x)

求解步骤

\frac{d}{d x} (tan^{n} (x))

使用连锁律:

n (tan (x))^{n - 1} \frac{d}{d x} (tan (x))

= n (tan (x))^{n - 1} \frac{d}{d x} (tan (x))

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

= n (tan (x))^{n - 1} sec^{2} (x)

化简

= n sec^{2} (x) tan^{n - 1} (x)

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