What is the derivative of arcsin(x/3) ?

The derivative of arcsin(x/3) is 1/(sqrt(9-x^2))

What is the first derivative of arcsin(x/3) ?

The first derivative of arcsin(x/3) is 1/(sqrt(9-x^2))

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\frac{d}{d x} (arcsin (\frac{x}{3}))

\frac{1}{9 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{3}))

Apply the chain rule:

\frac{1}{1 - ( \frac{x}{3} ) ^{2}} \frac{d}{d x} (\frac{x}{3})

= \frac{1}{1 - ( \frac{x}{3} ) ^{2}} \frac{d}{d x} (\frac{x}{3})

\frac{d}{d x} (\frac{x}{3}) = \frac{1}{3}

= \frac{1}{1 - ( \frac{x}{3} ) ^{2}} \cdot \frac{1}{3}

Simplify

\frac{1}{1 - ( \frac{x}{3} ) ^{2}} \cdot \frac{1}{3} : \frac{1}{9 - x ^{2}}

= \frac{1}{9 - x ^{2}}

What is the derivative of arcsin(x/3) ?
The derivative of arcsin(x/3) is 1/(sqrt(9-x^2))
What is the first derivative of arcsin(x/3) ?
The first derivative of arcsin(x/3) is 1/(sqrt(9-x^2))