What is the derivative of 1000sqrt(x^2-0.1x) ?

The derivative of 1000sqrt(x^2-0.1x) is (500(2x-0.1))/(sqrt(x^2-0.1x))

What is the first derivative of 1000sqrt(x^2-0.1x) ?

The first derivative of 1000sqrt(x^2-0.1x) is (500(2x-0.1))/(sqrt(x^2-0.1x))

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\frac{d}{d x} (1000 x^{2} - 0.1 x)

\frac{500 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

Solution steps

\frac{d}{d x} (1000 x^{2} - 0.1 x)

Take the constant out:

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

= 1000 \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

= 1000 \cdot \frac{1}{2 x ^{2} - 0.1 x} (2 x - 0.1)

Simplify

1000 \cdot \frac{1}{2 x ^{2} - 0.1 x} (2 x - 0.1) : \frac{500 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

= \frac{500 ( 2 x - 0.1 )}{x ^{2} - 0.1 x}

f (x) = \frac{8}{x}, at x = 25

x \to 0 lim (1 - 1 + x)

\int_{1}^{3} \frac{5}{x ^{2} + 4 x + 4} d x

\frac{d}{d x} (3 x^{2} e^{x} + e^{x} (x^{3} + 8))

\frac{d}{d y} (\frac{y ^{3}}{3})

What is the derivative of 1000sqrt(x^2-0.1x) ?
The derivative of 1000sqrt(x^2-0.1x) is (500(2x-0.1))/(sqrt(x^2-0.1x))
What is the first derivative of 1000sqrt(x^2-0.1x) ?
The first derivative of 1000sqrt(x^2-0.1x) is (500(2x-0.1))/(sqrt(x^2-0.1x))