What is the derivative of y=arcsin(1/(x^5)) ?

The derivative of y=arcsin(1/(x^5)) is -(5sqrt(x^{10)})/(x^6sqrt(x^{10)-1)}

What is the first derivative of y=arcsin(1/(x^5)) ?

The first derivative of y=arcsin(1/(x^5)) is -(5sqrt(x^{10)})/(x^6sqrt(x^{10)-1)}

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derivative of

y = arcsin (\frac{1}{x ^{5}})

- \frac{5 x ^{10}}{x ^{6} 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 ^{10}}{x ^{6} x ^{10} - 1}

= - \frac{5 x ^{10}}{x ^{6} x ^{10} - 1}

x \to 0 lim (\frac{ln ( 1 - 6 x )}{x})

x \to - 8 lim (\frac{∣ x + 8 ∣}{x + 8})

- \frac{4 x}{y}

f (x) = x cos (x)

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

What is the derivative of y=arcsin(1/(x^5)) ?
The derivative of y=arcsin(1/(x^5)) is -(5sqrt(x^{10)})/(x^6sqrt(x^{10)-1)}
What is the first derivative of y=arcsin(1/(x^5)) ?
The first derivative of y=arcsin(1/(x^5)) is -(5sqrt(x^{10)})/(x^6sqrt(x^{10)-1)}