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Popular >

derivative of arcsin(1/x)

Solution

derivative of

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}

Popular Examples

(\partial)/(\partial x)(ln(x^2+1)+y^2-z)

\frac{\partial}{\partial x} (ln (x^{2} + 1) + y^{2} - z)

(\partial)/(\partial x)(e^z(x-y)^2)

\frac{\partial}{\partial x} (e^{z} (x - y)^{2})

area x^2-4,y=0 area

x^{2} - 4, y = 0

integral of 64x^2cos(4x)

\int 64 x^{2} cos (4 x) d x

derivative of g(t)= 9/(sqrt(t))derivative of

g (t) = \frac{9}{t}

Frequently Asked Questions (FAQ)

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