What is the derivative of arccos(x-1) ?

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

What is the first derivative of arccos(x-1) ?

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

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\frac{d}{d x} (arccos (x - 1))

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

Solution steps

\frac{d}{d x} (arccos (x - 1))

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{- 15}^{0} \frac{1}{1 - x} d x

3 e^{- y} (x^{2} + y^{2}) + 4

\int (3 x^{2} - 5 x^{3} + 4) d x

\int (x^{3}) d x

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

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