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Popular Calculus >

derivative of arcsin(x/5)

Solution

derivative of

arcsin (\frac{x}{5})

Solution

\frac{1}{25 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{5}))

Apply the chain rule:

\frac{1}{1 - ( \frac{x}{5} ) ^{2}} \frac{d}{d x} (\frac{x}{5})

= \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \frac{d}{d x} (\frac{x}{5})

\frac{d}{d x} (\frac{x}{5}) = \frac{1}{5}

= \frac{1}{1 - ( \frac{x}{5} ) ^{2}} \cdot \frac{1}{5}

Simplify

\frac{1}{1 - ( \frac{x}{5} ) ^{2}} \cdot \frac{1}{5} : \frac{1}{25 - x ^{2}}

= \frac{1}{25 - x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x/5) ?
The derivative of arcsin(x/5) is 1/(sqrt(25-x^2))
What is the first derivative of arcsin(x/5) ?
The first derivative of arcsin(x/5) is 1/(sqrt(25-x^2))