What is the derivative of 1200sqrt(x^2-0.2x) ?

The derivative of 1200sqrt(x^2-0.2x) is (600(2x-0.2))/(sqrt(x^2-0.2x))

What is the first derivative of 1200sqrt(x^2-0.2x) ?

The first derivative of 1200sqrt(x^2-0.2x) is (600(2x-0.2))/(sqrt(x^2-0.2x))

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\frac{d}{d x} (1200 x^{2} - 0.2 x)

\frac{600 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

Solution steps

\frac{d}{d x} (1200 x^{2} - 0.2 x)

Take the constant out:

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

= 1200 \frac{d}{d x} (x^{2} - 0.2 x)

Apply the chain rule:

\frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

= \frac{1}{2 x ^{2} - 0.2 x} \frac{d}{d x} (x^{2} - 0.2 x)

\frac{d}{d x} (x^{2} - 0.2 x) = 2 x - 0.2

= 1200 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2)

Simplify

1200 \cdot \frac{1}{2 x ^{2} - 0.2 x} (2 x - 0.2) : \frac{600 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

= \frac{600 ( 2 x - 0.2 )}{x ^{2} - 0.2 x}

What is the derivative of 1200sqrt(x^2-0.2x) ?
The derivative of 1200sqrt(x^2-0.2x) is (600(2x-0.2))/(sqrt(x^2-0.2x))
What is the first derivative of 1200sqrt(x^2-0.2x) ?
The first derivative of 1200sqrt(x^2-0.2x) is (600(2x-0.2))/(sqrt(x^2-0.2x))