What is the derivative of x/(sqrt(9-x^2)) ?

The derivative of x/(sqrt(9-x^2)) is 9/((9-x^2)sqrt(9-x^2))

What is the first derivative of x/(sqrt(9-x^2)) ?

The first derivative of x/(sqrt(9-x^2)) is 9/((9-x^2)sqrt(9-x^2))

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derivative of

\frac{x}{9 - x ^{2}}

\frac{9}{( 9 - x ^{2} ) 9 - x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{9 - x ^{2}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d x}{d x} 9 - x ^{2} - \frac{d}{d x} ( 9 - x ^{2} ) x}{( 9 - x ^{2} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (9 - x^{2}) = - \frac{x}{9 - x ^{2}}

= \frac{1 \cdot 9 - x ^{2} - ( - \frac{x}{9 - x ^{2}} ) x}{( 9 - x ^{2} ) ^{2}}

Simplify

\frac{1 \cdot 9 - x ^{2} - ( - \frac{x}{9 - x ^{2}} ) x}{( 9 - x ^{2} ) ^{2}} : \frac{9}{( 9 - x ^{2} ) 9 - x ^{2}}

= \frac{9}{( 9 - x ^{2} ) 9 - x ^{2}}

x \to - 3 lim (- 1.2 x - 4.6)

\frac{d}{d x} (\frac{x ^{2}}{1 + 6 x})

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\frac{d}{d x} (- 4 tan (x) - csc (x))

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What is the derivative of x/(sqrt(9-x^2)) ?
The derivative of x/(sqrt(9-x^2)) is 9/((9-x^2)sqrt(9-x^2))
What is the first derivative of x/(sqrt(9-x^2)) ?
The first derivative of x/(sqrt(9-x^2)) is 9/((9-x^2)sqrt(9-x^2))