What is the derivative of arccos(-2x) ?

The derivative of arccos(-2x) is 2/(sqrt(1-4x^2))

What is the first derivative of arccos(-2x) ?

The first derivative of arccos(-2x) is 2/(sqrt(1-4x^2))

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\frac{d}{d x} (arccos (- 2 x))

\frac{2}{1 - 4 x ^{2}}

Solution steps

\frac{d}{d x} (arccos (- 2 x))

Apply the chain rule:

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

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

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

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

Simplify

- \frac{1}{1 - ( - 2 x ) ^{2}} (- 2) : \frac{2}{1 - 4 x ^{2}}

= \frac{2}{1 - 4 x ^{2}}

What is the derivative of arccos(-2x) ?
The derivative of arccos(-2x) is 2/(sqrt(1-4x^2))
What is the first derivative of arccos(-2x) ?
The first derivative of arccos(-2x) is 2/(sqrt(1-4x^2))