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Popular >

derivative of arcsin(x/3)

Solution

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

Solution

\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}}

Popular Examples

integral of sqrt((4x+1)/(4x))

\int \frac{4 x + 1}{4 x} d x

derivative of (1-3x/(1+3x))

\frac{d}{d x} (\frac{1 - 3 x}{1 + 3 x})

sum from n=1 to infinity of 1/(n^2)-1/n

n = 1 \sum \infty \frac{1}{n ^{2}} - \frac{1}{n}

sum from n=2 to infinity of n/(n+1)

n = 2 \sum \infty \frac{n}{n + 1}

limit as x approaches 5 of sqrt(x^2-25)

x \to 5 lim (x^{2} - 25)

Frequently Asked Questions (FAQ)

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))