What is the derivative of (cos(x)^{-1}) ?

The derivative of (cos(x)^{-1}) is sec(x)tan(x)

What is the first derivative of (cos(x)^{-1}) ?

The first derivative of (cos(x)^{-1}) is sec(x)tan(x)

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\frac{d}{d x} ((cos (x))^{- 1})

sec (x) tan (x)

Solution steps

\frac{d}{d x} ((cos (x))^{- 1})

Apply the chain rule:

- \frac{1}{( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

= - \frac{1}{( cos ( x ) ) ^{2}} \frac{d}{d x} (cos (x))

\frac{d}{d x} (cos (x)) = - sin (x)

= - \frac{1}{( cos ( x ) ) ^{2}} (- sin (x))

Simplify

- \frac{1}{cos ^{2} ( x )} (- sin (x)) : sec (x) tan (x)

= sec (x) tan (x)

\int (- 14 sin (x)) d x

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

\int_{0}^{\infty} e^{- 0.4 x} d x

\int e^{x} + e^{- x} d x

\int (2 x y + 4 x^{3}) d x

What is the derivative of (cos(x)^{-1}) ?
The derivative of (cos(x)^{-1}) is sec(x)tan(x)
What is the first derivative of (cos(x)^{-1}) ?
The first derivative of (cos(x)^{-1}) is sec(x)tan(x)