What is the derivative of-arcsin((sqrt(a^2-x^2)/a)) ?

The derivative of-arcsin((sqrt(a^2-x^2)/a)) is 1/(sqrt(a^2-x^2))

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

The first derivative of-arcsin((sqrt(a^2-x^2)/a)) is 1/(sqrt(a^2-x^2))

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\frac{d}{d x} (- arcsin (\frac{a ^{2} - x ^{2}}{a}))

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

Solution steps

\frac{d}{d x} (- arcsin (\frac{a ^{2} - x ^{2}}{a}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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