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Popular >

derivative of arcsin((ax/4))

Solution

\frac{d}{d x} (arcsin (\frac{a x}{4}))

Solution

\frac{a}{16 - a ^{2} x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{a x}{4}))

Apply the chain rule:

\frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \frac{d}{d x} (\frac{a x}{4})

= \frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \frac{d}{d x} (\frac{a x}{4})

\frac{d}{d x} (\frac{a x}{4}) = \frac{a}{4}

= \frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \cdot \frac{a}{4}

Simplify

\frac{1}{1 - ( \frac{a x}{4} ) ^{2}} \cdot \frac{a}{4} : \frac{a}{16 - a ^{2} x ^{2}}

= \frac{a}{16 - a ^{2} x ^{2}}

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\int \frac{a}{2} x + \frac{a}{2} d x

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Frequently Asked Questions (FAQ)

What is the derivative of arcsin((ax/4)) ?
The derivative of arcsin((ax/4)) is a/(sqrt(16-a^2x^2))
What is the first derivative of arcsin((ax/4)) ?
The first derivative of arcsin((ax/4)) is a/(sqrt(16-a^2x^2))