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Popular >

derivative of arcsin(1/(x^5))

Solution

\frac{d}{d x} (arcsin (\frac{1}{x ^{5}}))

Solution

- \frac{5}{x x ^{10} - 1}

Solution steps

\frac{d}{d x} (arcsin (\frac{1}{x ^{5}}))

Apply the chain rule:

\frac{1}{1 - ( \frac{1}{x ^{5}} ) ^{2}} \frac{d}{d x} (\frac{1}{x ^{5}})

= \frac{1}{1 - ( \frac{1}{x ^{5}} ) ^{2}} \frac{d}{d x} (\frac{1}{x ^{5}})

\frac{d}{d x} (\frac{1}{x ^{5}}) = - \frac{5}{x ^{6}}

= \frac{1}{1 - ( \frac{1}{x ^{5}} ) ^{2}} (- \frac{5}{x ^{6}})

Simplify

\frac{1}{1 - ( \frac{1}{x ^{5}} ) ^{2}} (- \frac{5}{x ^{6}}) : - \frac{5}{x x ^{10} - 1}

= - \frac{5}{x x ^{10} - 1}

Popular Examples

derivative of (1-e^z)(z+e^z)derivative of

(1 - e^{z}) (z + e^{z})

y^'=((y^2+x^2))/(2xy)

y^{^{'}} = \frac{( y ^{2} + x ^{2} )}{2 x y}

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f (x) = sin (x) + \frac{1}{2}, at (x = 0)

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\int_{1}^{5} 9 3 v + 1 d v

derivative of cos(2x+2xsin(2x))

\frac{d}{d x} (cos (2 x) + 2 x sin (2 x))

Frequently Asked Questions (FAQ)

What is the derivative of arcsin(1/(x^5)) ?
The derivative of arcsin(1/(x^5)) is -5/(xsqrt(x^{10)-1)}
What is the first derivative of arcsin(1/(x^5)) ?
The first derivative of arcsin(1/(x^5)) is -5/(xsqrt(x^{10)-1)}