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Popular >

derivative of arccos(1/x)

Solution

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

Solution

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

Solution steps

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

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

Popular Examples

derivative of (4x-3^{2x+1})

\frac{d}{d x} ((4 x - 3)^{2 x + 1})

derivative of x/4 derivative of

\frac{x}{4}

limit as x approaches-7 of (x^2-9)/(7-x)

x \to - 7 lim (\frac{x ^{2} - 9}{7 - x})

integral of 1/(xsqrt(4x^2-1))

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

limit as x approaches 1+of arctan(ln(x-1))

x \to 1 + lim (arctan (ln (x - 1)))

Frequently Asked Questions (FAQ)

What is the derivative of arccos(1/x) ?
The derivative of arccos(1/x) is 1/(xsqrt(x^2-1))
What is the first derivative of arccos(1/x) ?
The first derivative of arccos(1/x) is 1/(xsqrt(x^2-1))