What is the derivative of cos^{-2}(x) ?

The derivative of cos^{-2}(x) is 2sec^2(x)tan(x)

What is the first derivative of cos^{-2}(x) ?

The first derivative of cos^{-2}(x) is 2sec^2(x)tan(x)

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\frac{d}{d x} (cos^{- 2} (x))

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

Solution steps

\frac{d}{d x} (cos^{- 2} (x))

Simplify

cos^{- 2} (x) : sec^{2} (x)

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

Apply the chain rule:

2 sec (x) \frac{d}{d x} (sec (x))

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

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

= 2 sec (x) sec (x) tan (x)

Simplify

2 sec (x) sec (x) tan (x) : 2 sec^{2} (x) tan (x)

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

\frac{d}{d x} ((3 x^{2} + 7 x)^{4})

f (x) = x^{3} - 9 x, at x = 3

\int (1 + \frac{1}{x})^{2} \frac{1}{x ^{2}} d x

\frac{d}{d x} (arccos (3 x + 1))

\int 3^{x} x d x

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