What is the derivative of (6x-x^2^{1/2}) ?

The derivative of (6x-x^2^{1/2}) is (3-x)/((6x-x^2)^{1/2)}

What is the first derivative of (6x-x^2^{1/2}) ?

The first derivative of (6x-x^2^{1/2}) is (3-x)/((6x-x^2)^{1/2)}

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\frac{d}{d x} ((6 x - x^{2})^{\frac{1}{2}})

\frac{3 - x}{( 6 x - x ^{2} ) ^{\frac{1}{2}}}

Solution steps

\frac{d}{d x} ((6 x - x^{2})^{\frac{1}{2}})

Apply the chain rule:

\frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x - x^{2})

= \frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} \frac{d}{d x} (6 x - x^{2})

\frac{d}{d x} (6 x - x^{2}) = 6 - 2 x

= \frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} (6 - 2 x)

Simplify

\frac{1}{2 ( 6 x - x ^{2} ) ^{\frac{1}{2}}} (6 - 2 x) : \frac{3 - x}{( 6 x - x ^{2} ) ^{\frac{1}{2}}}

= \frac{3 - x}{( 6 x - x ^{2} ) ^{\frac{1}{2}}}

What is the derivative of (6x-x^2^{1/2}) ?
The derivative of (6x-x^2^{1/2}) is (3-x)/((6x-x^2)^{1/2)}
What is the first derivative of (6x-x^2^{1/2}) ?
The first derivative of (6x-x^2^{1/2}) is (3-x)/((6x-x^2)^{1/2)}