derivative of sec^{11}(x)

解答

\frac{d}{d x} (sec^{11} (x))

11 sec^{11} (x) tan (x)

求解步骤

\frac{d}{d x} (sec^{11} (x))

使用连锁律:

11 (sec (x))^{10} \frac{d}{d x} (sec (x))

= 11 (sec (x))^{10} \frac{d}{d x} (sec (x))

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

= 11 (sec (x))^{10} sec (x) tan (x)

化简

11 sec^{10} (x) sec (x) tan (x) : 11 sec^{11} (x) tan (x)

= 11 sec^{11} (x) tan (x)

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