What is the derivative of sec^n(x) ?

The derivative of sec^n(x) is ntan(x)sec^n(x)

What is the first derivative of sec^n(x) ?

The first derivative of sec^n(x) is ntan(x)sec^n(x)

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

What is the derivative of sec^n(x) ?
The derivative of sec^n(x) is ntan(x)sec^n(x)
What is the first derivative of sec^n(x) ?
The first derivative of sec^n(x) is ntan(x)sec^n(x)