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Popular >

derivative of sqrt(2x-x^2)

Solution

derivative of

2 x - x^{2}

Solution

\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}}

Popular Examples

limit as x approaches infinity of (2x^3+3x-4)/(5-4x^3)

x \to \infty lim (\frac{2 x ^{3} + 3 x - 4}{5 - 4 x ^{3}})

f^{^{'}} (x) = x^{2} e^{x}

derivative of (6x^{3/2}/x)

\frac{d}{d x} (\frac{6 x ^{\frac{3}{2}}}{x})

limit as x approaches 1/4 of x^2-x+9/16

x \to \frac{1}{4} lim (x^{2} - x + \frac{9}{16})

integral of sqrt(1+81x)

\int 1 + 81 x d x

Frequently Asked Questions (FAQ)

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