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Popular >

derivative of arcsin(sqrt(x^2-4))

Solution

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

Solution

\frac{x}{- x ^{2} + 5 x ^{2} - 4}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - ( x ^{2} - 4 ) ^{2}} \cdot \frac{x}{x ^{2} - 4} : \frac{x}{- x ^{2} + 5 x ^{2} - 4}

= \frac{x}{- x ^{2} + 5 x ^{2} - 4}

Popular Examples

y=e^{-2((x-146)-2((ln(19.52))/2))}

y = e^{- 2 ((x - 146) - 2 (\frac{l n ( 19.52 )}{2}))}

integral from 0 to 3 of (x-1)

\int_{0}^{3} (x - 1) d x

integral of (3x^2-7x+4)

\int (3 x^{2} - 7 x + 4) d x

integral of (3x^39x^2-15)/(x^24x^4)

\int \frac{3 x ^{3} 9 x ^{2} - 15}{x ^{2} 4 x ^{4}} d x

derivative of arcsin(3x+y)

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

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(sqrt(x^2-4)) ?
The derivative of arcsin(sqrt(x^2-4)) is x/(sqrt(-x^2+5)\sqrt{x^2-4)}
What is the first derivative of arcsin(sqrt(x^2-4)) ?
The first derivative of arcsin(sqrt(x^2-4)) is x/(sqrt(-x^2+5)\sqrt{x^2-4)}