What is the derivative of sqrt(4x^2-8x) ?

The derivative of sqrt(4x^2-8x) is (2(x-1))/(sqrt(x(x-2)))

What is the first derivative of sqrt(4x^2-8x) ?

The first derivative of sqrt(4x^2-8x) is (2(x-1))/(sqrt(x(x-2)))

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

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

Solution steps

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

Apply the chain rule:

\frac{1}{2 4 x ^{2} - 8 x} \frac{d}{d x} (4 x^{2} - 8 x)

= \frac{1}{2 4 x ^{2} - 8 x} \frac{d}{d x} (4 x^{2} - 8 x)

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

= \frac{1}{2 4 x ^{2} - 8 x} (8 x - 8)

Simplify

\frac{1}{2 4 x ^{2} - 8 x} (8 x - 8) : \frac{2 ( x - 1 )}{x ( x - 2 )}

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

What is the derivative of sqrt(4x^2-8x) ?
The derivative of sqrt(4x^2-8x) is (2(x-1))/(sqrt(x(x-2)))
What is the first derivative of sqrt(4x^2-8x) ?
The first derivative of sqrt(4x^2-8x) is (2(x-1))/(sqrt(x(x-2)))