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

The derivative of 1/(sqrt(a^2-x^2)) is x/((a^2-x^2)^{3/2)}

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

The first derivative of 1/(sqrt(a^2-x^2)) is x/((a^2-x^2)^{3/2)}

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

\frac{x}{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{1}{2 ( a ^{2} - x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (a^{2} - x^{2})

= - \frac{1}{2 ( a ^{2} - x ^{2} ) ^{\frac{3}{2}}} \frac{d}{d x} (a^{2} - x^{2})

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

= - \frac{1}{2 ( a ^{2} - x ^{2} ) ^{\frac{3}{2}}} (- 2 x)

Simplify

- \frac{1}{2 ( a ^{2} - x ^{2} ) ^{\frac{3}{2}}} (- 2 x) : \frac{x}{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}}

= \frac{x}{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}}

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What is the derivative of 1/(sqrt(a^2-x^2)) ?
The derivative of 1/(sqrt(a^2-x^2)) is x/((a^2-x^2)^{3/2)}
What is the first derivative of 1/(sqrt(a^2-x^2)) ?
The first derivative of 1/(sqrt(a^2-x^2)) is x/((a^2-x^2)^{3/2)}