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Popular Calculus >

derivative of 2arcsin(x-1)

Solution

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

Solution

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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

Simplify

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

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

Graph

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in v erse l a pl a ce \frac{20}{s ( s ^{2} + 6 s + 144 )}

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a re a y = \frac{3}{x}, y = \frac{3}{x ^{2}}, x = 4

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d er i v a t i v e f (x) = 800 - 800 x^{- 1}

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d er i v a t i v e y = \frac{2 x + 5}{x}

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\frac{d}{d x} (arccos (- \frac{x}{5}))

Frequently Asked Questions (FAQ)

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