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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\int_{0}^{π} (8 + 5 sin (x)) d x

x \to - \infty lim (0 - x)

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

\int_{0}^{1} \frac{3}{2} x d x

x^{2} \frac{d y}{d x} - x y = 4 x^{3} sin (x)

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