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Popular Calculus >

derivative of f(x)=sqrt(8x-x^2)

Solution

derivative of

f (x) = 8 x - x^{2}

Solution

\frac{4 - x}{8 x - x ^{2}}

Solution steps

\frac{d}{d x} (8 x - x^{2})

Apply the chain rule:

\frac{1}{2 8 x - x ^{2}} \frac{d}{d x} (8 x - x^{2})

= \frac{1}{2 8 x - x ^{2}} \frac{d}{d x} (8 x - x^{2})

\frac{d}{d x} (8 x - x^{2}) = 8 - 2 x

= \frac{1}{2 8 x - x ^{2}} (8 - 2 x)

Simplify

\frac{1}{2 8 x - x ^{2}} (8 - 2 x) : \frac{4 - x}{8 x - x ^{2}}

= \frac{4 - x}{8 x - x ^{2}}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=sqrt(8x-x^2) ?
The derivative of f(x)=sqrt(8x-x^2) is (4-x)/(sqrt(8x-x^2))
What is the first derivative of f(x)=sqrt(8x-x^2) ?
The first derivative of f(x)=sqrt(8x-x^2) is (4-x)/(sqrt(8x-x^2))