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Popular >

derivative of sqrt(2ax-x^2)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

area x=((y-3)^2)/5 ,x=13-y area

x = \frac{( y - 3 ) ^{2}}{5}, x = 13 - y

derivative of 3/4 x^{1/2}

\frac{d}{d x} (\frac{3}{4} x^{\frac{1}{2}})

integral from 0 to 8 of 9/(10x^2+11x+1)

\int_{0}^{8} \frac{9}{10 x ^{2} + 11 x + 1} d x

(dy)/(dx)=(x^2)/(6e^y)

\frac{d y}{d x} = \frac{x ^{2}}{6 e ^{y}}

derivative of f(x)=4x^2-7x derivative of

f (x) = 4 x^{2} - 7 x

Frequently Asked Questions (FAQ)

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