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Popular >

derivative of sqrt(18x-x^2)

Solution

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

Solution

\frac{9 - x}{18 x - x ^{2}}

Solution steps

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

Apply the chain rule:

\frac{1}{2 18 x - x ^{2}} \frac{d}{d x} (18 x - x^{2})

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

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

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

Simplify

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

= \frac{9 - x}{18 x - x ^{2}}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(18x-x^2) ?
The derivative of sqrt(18x-x^2) is (9-x)/(sqrt(18x-x^2))
What is the first derivative of sqrt(18x-x^2) ?
The first derivative of sqrt(18x-x^2) is (9-x)/(sqrt(18x-x^2))