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))

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

\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}

\int (2 e^{5 x}) d x

\frac{x}{( x + 1 ) ^{2}}

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

\frac{d}{d x} (arctan (\frac{x}{y}))

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

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))