What is the derivative of 800sqrt(x^2-0.1x) ?

The derivative of 800sqrt(x^2-0.1x) is (400(2x-0.1))/(sqrt(x^2-0.1x))

What is the first derivative of 800sqrt(x^2-0.1x) ?

The first derivative of 800sqrt(x^2-0.1x) is (400(2x-0.1))/(sqrt(x^2-0.1x))

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\frac{d}{d x} (800 x^{2} - 0.1 x)

\frac{400 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

Solution steps

\frac{d}{d x} (800 x^{2} - 0.1 x)

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 800 \frac{d}{d x} (x^{2} - 0.1 x)

Apply the chain rule:

\frac{1}{2 x ^{2} - 0.1 x} \frac{d}{d x} (x^{2} - 0.1 x)

= \frac{1}{2 x ^{2} - 0.1 x} \frac{d}{d x} (x^{2} - 0.1 x)

\frac{d}{d x} (x^{2} - 0.1 x) = 2 x - 0.1

= 800 \cdot \frac{1}{2 x ^{2} - 0.1 x} (2 x - 0.1)

Simplify

800 \cdot \frac{1}{2 x ^{2} - 0.1 x} (2 x - 0.1) : \frac{400 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

= \frac{400 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

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x \to 0 lim (\frac{x ^{2} + 1}{x - 1})

(x + y + 1) d x - (y - x + 3) d y = 0

What is the derivative of 800sqrt(x^2-0.1x) ?
The derivative of 800sqrt(x^2-0.1x) is (400(2x-0.1))/(sqrt(x^2-0.1x))
What is the first derivative of 800sqrt(x^2-0.1x) ?
The first derivative of 800sqrt(x^2-0.1x) is (400(2x-0.1))/(sqrt(x^2-0.1x))