What is the derivative of (2x^2-4x^{1/2}) ?

The derivative of (2x^2-4x^{1/2}) is (2(x-1))/((2x^2-4x)^{1/2)}

What is the first derivative of (2x^2-4x^{1/2}) ?

The first derivative of (2x^2-4x^{1/2}) is (2(x-1))/((2x^2-4x)^{1/2)}

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

\frac{2 ( x - 1 )}{( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (2 x^{2} - 4 x) = 4 x - 4

= \frac{1}{2 ( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}} (4 x - 4)

Simplify

\frac{1}{2 ( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}} (4 x - 4) : \frac{2 ( x - 1 )}{( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}}

= \frac{2 ( x - 1 )}{( 2 x ^{2} - 4 x ) ^{\frac{1}{2}}}

What is the derivative of (2x^2-4x^{1/2}) ?
The derivative of (2x^2-4x^{1/2}) is (2(x-1))/((2x^2-4x)^{1/2)}
What is the first derivative of (2x^2-4x^{1/2}) ?
The first derivative of (2x^2-4x^{1/2}) is (2(x-1))/((2x^2-4x)^{1/2)}