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Popular >

derivative of y=arcsin(1/x)

Solution

derivative of

y = arcsin (\frac{1}{x})

Solution

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

Solution steps

\frac{d}{d x} (arcsin (\frac{1}{x}))

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of 5ln(x^2-x+12)

\int 5 ln (x^{2} - x + 12) d x

integral from 2 to 3 of (17)/(sqrt(3-x))

\int_{2}^{3} \frac{17}{3 - x} d x

integral of 1/(x^2sqrt(25-x^2))x)

\int \frac{1}{x ^{2} 25 - x ^{2}} d (x) d x

integral from 0 to 1 of (97)/(x^5)

\int_{0}^{1} \frac{97}{x ^{5}} d x

(dN)/(dt)=0.2(4000-N)

\frac{d N}{d t} = 0.2 (4000 - N)

Frequently Asked Questions (FAQ)

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