What is the derivative of 5arcsin((x-1)/(x+1)) ?

The derivative of 5arcsin((x-1)/(x+1)) is (5sqrt((x+1)^2))/(sqrt(x)(x+1)^2)

What is the first derivative of 5arcsin((x-1)/(x+1)) ?

The first derivative of 5arcsin((x-1)/(x+1)) is (5sqrt((x+1)^2))/(sqrt(x)(x+1)^2)

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derivative of

5 arcsin (\frac{x - 1}{x + 1})

\frac{5 ( x + 1 ) ^{2}}{x ( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (5 arcsin (\frac{x - 1}{x + 1}))

Take the constant out:

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

= 5 \frac{d}{d x} (arcsin (\frac{x - 1}{x + 1}))

Apply the chain rule:

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

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

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

= 5 \cdot \frac{1}{1 - ( \frac{x - 1}{x + 1} ) ^{2}} \cdot \frac{2}{( x + 1 ) ^{2}}

Simplify

5 \cdot \frac{1}{1 - ( \frac{x - 1}{x + 1} ) ^{2}} \cdot \frac{2}{( x + 1 ) ^{2}} : \frac{5 ( x + 1 ) ^{2}}{x ( x + 1 ) ^{2}}

= \frac{5 ( x + 1 ) ^{2}}{x ( x + 1 ) ^{2}}

What is the derivative of 5arcsin((x-1)/(x+1)) ?
The derivative of 5arcsin((x-1)/(x+1)) is (5sqrt((x+1)^2))/(sqrt(x)(x+1)^2)
What is the first derivative of 5arcsin((x-1)/(x+1)) ?
The first derivative of 5arcsin((x-1)/(x+1)) is (5sqrt((x+1)^2))/(sqrt(x)(x+1)^2)