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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derivative of

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}}

\frac{d ^{4}}{d x ^{4}} (cos (3 x))

n = 0 \sum \infty - 1

\int_{- 3}^{3} x 9 - x^{2} d x

\int tan^{4} (θ) sec^{6} (θ) d θ

y = 5 x, y = 3 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))