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Popular >

derivative of arccos(7/x)

Solution

\frac{d}{d x} (arccos (\frac{7}{x}))

Solution

\frac{7}{x x ^{2} - 49}

Solution steps

\frac{d}{d x} (arccos (\frac{7}{x}))

Apply the chain rule:

- \frac{1}{1 - ( \frac{7}{x} ) ^{2}} \frac{d}{d x} (\frac{7}{x})

= - \frac{1}{1 - ( \frac{7}{x} ) ^{2}} \frac{d}{d x} (\frac{7}{x})

\frac{d}{d x} (\frac{7}{x}) = - \frac{7}{x ^{2}}

= - \frac{1}{1 - ( \frac{7}{x} ) ^{2}} (- \frac{7}{x ^{2}})

Simplify

- \frac{1}{1 - ( \frac{7}{x} ) ^{2}} (- \frac{7}{x ^{2}}) : \frac{7}{x x ^{2} - 49}

= \frac{7}{x x ^{2} - 49}

Popular Examples

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

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\int \frac{5 x + 7}{x ^{2} + 4 x + 4} d x

integral of (e^{-cot(z)})/(sin^2(z))

\int \frac{e ^{- c o t (z)}}{sin ^{2} ( z )} d z

(d^2)/(dx^2)((x^2)/((2+x)))

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{( 2 + x )})

derivative of (x^2/(y^2))

\frac{d}{d x} (\frac{x ^{2}}{y ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of arccos(7/x) ?
The derivative of arccos(7/x) is 7/(xsqrt(x^2-49))
What is the first derivative of arccos(7/x) ?
The first derivative of arccos(7/x) is 7/(xsqrt(x^2-49))