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Popular >

derivative of arcsin(x^2-3)

Solution

\frac{d}{d x} (arcsin (x^{2} - 3))

Solution

\frac{2 x}{- x ^{4} + 6 x ^{2} - 8}

Solution steps

\frac{d}{d x} (arcsin (x^{2} - 3))

Apply the chain rule:

\frac{1}{1 - ( x ^{2} - 3 ) ^{2}} \frac{d}{d x} (x^{2} - 3)

= \frac{1}{1 - ( x ^{2} - 3 ) ^{2}} \frac{d}{d x} (x^{2} - 3)

\frac{d}{d x} (x^{2} - 3) = 2 x

= \frac{1}{1 - ( x ^{2} - 3 ) ^{2}} \cdot 2 x

Simplify

\frac{1}{1 - ( x ^{2} - 3 ) ^{2}} \cdot 2 x : \frac{2 x}{- x ^{4} + 6 x ^{2} - 8}

= \frac{2 x}{- x ^{4} + 6 x ^{2} - 8}

Popular Examples

integral of 2/((1-x^2)^{3/2)}

\int \frac{2}{( 1 - x ^{2} ) ^{\frac{3}{2}}} d x

inverse oflaplace 1/((s*(s+1)))inverse laplace

\frac{1}{( s \cdot ( s + 1 ) )}

integral of (x^2)/(16+9x^2)

\int \frac{x ^{2}}{16 + 9 x ^{2}} d x

integral from 1 to 2 of 2x-x^2

\int_{1}^{2} 2 x - x^{2} d x

integral of 1/(x^2-2x+37)

\int \frac{1}{x ^{2} - 2 x + 37} d x

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(x^2-3) ?
The derivative of arcsin(x^2-3) is (2x)/(sqrt(-x^4+6x^2-8))
What is the first derivative of arcsin(x^2-3) ?
The first derivative of arcsin(x^2-3) is (2x)/(sqrt(-x^4+6x^2-8))