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

The derivative of y=sqrt(2x-x^2) is (1-x)/(sqrt(2x-x^2))

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

The first derivative of y=sqrt(2x-x^2) is (1-x)/(sqrt(2x-x^2))

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derivative of

y = 2 x - x^{2}

\frac{1 - x}{2 x - x ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1 - x}{2 x - x ^{2}}

What is the derivative of y=sqrt(2x-x^2) ?
The derivative of y=sqrt(2x-x^2) is (1-x)/(sqrt(2x-x^2))
What is the first derivative of y=sqrt(2x-x^2) ?
The first derivative of y=sqrt(2x-x^2) is (1-x)/(sqrt(2x-x^2))