What is the derivative of arcsin(x/pi) ?

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

What is the first derivative of arcsin(x/pi) ?

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

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\frac{d}{d x} (arcsin (\frac{x}{π}))

\frac{1}{π ^{2} - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{π}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{π}) = \frac{1}{π}

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

Simplify

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

= \frac{1}{π ^{2} - x ^{2}}

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