What is the derivative of (2x-x^2^{1/2}) ?

The derivative of (2x-x^2^{1/2}) is (1-x)/((2x-x^2)^{1/2)}

What is the first derivative of (2x-x^2^{1/2}) ?

The first derivative of (2x-x^2^{1/2}) is (1-x)/((2x-x^2)^{1/2)}

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

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

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{( x - y )}{( x + y )})

\frac{\partial}{\partial x} (e^{x + y + 3})

(\frac{x ^{3}}{3})^{^{'}}

y^{^{'}} = (x + 1) (3 y - 1) 2

\frac{d}{d x} (\frac{8 x + x ^{2}}{( 4 + x ) ^{2}})

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