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Popular >

derivative of sqrt(r^2-9x^2)

Solution

derivative of

r^{2} - 9 x^{2}

Solution

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (r^{2} - 9 x^{2}) = - 18 x

= \frac{1}{2 r ^{2} - 9 x ^{2}} (- 18 x)

Simplify

\frac{1}{2 r ^{2} - 9 x ^{2}} (- 18 x) : - \frac{9 x}{r ^{2} - 9 x ^{2}}

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

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Frequently Asked Questions (FAQ)

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