What is the derivative of arccos(cos(x)) ?

The derivative of arccos(cos(x)) is csc(x)sqrt(sin^2(x))

What is the first derivative of arccos(cos(x)) ?

The first derivative of arccos(cos(x)) is csc(x)sqrt(sin^2(x))

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\frac{d}{d x} (arccos (cos (x)))

csc (x) sin^{2} (x)

Solution steps

\frac{d}{d x} (arccos (cos (x)))

Apply the chain rule:

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

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

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

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

Simplify

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

= csc (x) sin^{2} (x)

\frac{d y}{d x}, x y = x - 2 y

\frac{d y}{d x} = \frac{( x - 3 )}{y - 4}

\int \frac{289}{x ^{3} - 17 x ^{2}} d x

\int (1 - t) d t

x \to 0 + lim (I n x)

What is the derivative of arccos(cos(x)) ?
The derivative of arccos(cos(x)) is csc(x)sqrt(sin^2(x))
What is the first derivative of arccos(cos(x)) ?
The first derivative of arccos(cos(x)) is csc(x)sqrt(sin^2(x))