What is the derivative of ((x^2+4)/x) ?

The derivative of ((x^2+4)/x) is (x^2-4)/(x^2)

What is the first derivative of ((x^2+4)/x) ?

The first derivative of ((x^2+4)/x) is (x^2-4)/(x^2)

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\frac{d}{d x} (\frac{( x ^{2} + 4 )}{x})

\frac{x ^{2} - 4}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} + 4 )}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= \frac{x ^{2} - 4}{x ^{2}}

y = 2 x^{3} - 8 x, (2, 0)

\frac{d v}{d t} = - v

\int s h \frac{x}{3} d x

f (x) = 4 x^{2} - 8, at 3

n = 1 \sum \infty \frac{3}{n}

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