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Popular >

derivative of sec^{n-2}(x)

Solution

\frac{d}{d x} (sec^{n - 2} (x))

Solution

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

Solution steps

\frac{d}{d x} (sec^{n - 2} (x))

Apply the chain rule:

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

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

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

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

Simplify

sec^{n - 3} (x) (n - 2) sec (x) tan (x) : tan (x) sec^{n - 2} (x) (n - 2)

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

Popular Examples

limit as x approaches 0 of (10^x-1)/x

x \to 0 lim (\frac{1 0 ^{x} - 1}{x})

derivative of (x^4+2)^2(x^5+4)^4 derivative of

(x^{4} + 2)^{2} (x^{5} + 4)^{4}

derivative of x^2-2x+5 derivative of

x^{2} - 2 x + 5

integral from-infinity to 8 of xe^{x/4}

\int_{- \infty}^{8} x e^{\frac{x}{4}} d x

tangent of f(x)=2x^4-11x^2,\at x=1 tangent of

f (x) = 2 x^{4} - 11 x^{2}, at x = 1

Frequently Asked Questions (FAQ)

What is the derivative of sec^{n-2}(x) ?
The derivative of sec^{n-2}(x) is tan(x)sec^{n-2}(x)(n-2)
What is the first derivative of sec^{n-2}(x) ?
The first derivative of sec^{n-2}(x) is tan(x)sec^{n-2}(x)(n-2)