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Popular >

derivative of arcsin(x/2)

Solution

derivative of

arcsin (\frac{x}{2})

Solution

\frac{1}{4 - x ^{2}}

Solution steps

\frac{d}{d x} (arcsin (\frac{x}{2}))

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{2}

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

Simplify

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

= \frac{1}{4 - x ^{2}}

Graph

Popular Examples

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\int \frac{12}{x ^{5}} d x

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n \to \infty lim (e^{3 n^{2}})

(\partial)/(\partial y)(sqrt(17-x^2-4y^2))

\frac{\partial}{\partial y} (17 - x^{2} - 4 y^{2})

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\frac{d}{d x} (a e^{\frac{x}{2}} + b e^{- x})

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x/2) ?
The derivative of arcsin(x/2) is 1/(sqrt(4-x^2))
What is the first derivative of arcsin(x/2) ?
The first derivative of arcsin(x/2) is 1/(sqrt(4-x^2))