What is the derivative of arcsin((x-2/1)) ?

The derivative of arcsin((x-2/1)) is 1/(sqrt(-x^2+4x-3))

What is the first derivative of arcsin((x-2/1)) ?

The first derivative of arcsin((x-2/1)) is 1/(sqrt(-x^2+4x-3))

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

\frac{1}{- x ^{2} + 4 x - 3}

Solution steps

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

Simplify

arcsin (\frac{x - 2}{1}) : arcsin (x - 2)

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - ( x - 2 ) ^{2}} \cdot 1 : \frac{1}{- x ^{2} + 4 x - 3}

= \frac{1}{- x ^{2} + 4 x - 3}

What is the derivative of arcsin((x-2/1)) ?
The derivative of arcsin((x-2/1)) is 1/(sqrt(-x^2+4x-3))
What is the first derivative of arcsin((x-2/1)) ?
The first derivative of arcsin((x-2/1)) is 1/(sqrt(-x^2+4x-3))