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

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

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

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

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derivative of

g (x) = 9 - x^{2}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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