What is the derivative of (x^2+5)/x ?

The derivative of (x^2+5)/x is (x^2-5)/(x^2)

What is the first derivative of (x^2+5)/x ?

The first derivative of (x^2+5)/x is (x^2-5)/(x^2)

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derivative of

\frac{x ^{2} + 5}{x}

\frac{x ^{2} - 5}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 5}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 5 ) x - \frac{d x}{d x} ( x ^{2} + 5 )}{x ^{2}}

\frac{d}{d x} (x^{2} + 5) = 2 x

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

= \frac{2 xx - 1 \cdot ( x ^{2} + 5 )}{x ^{2}}

Simplify

\frac{2 xx - 1 \cdot ( x ^{2} + 5 )}{x ^{2}} : \frac{x ^{2} - 5}{x ^{2}}

= \frac{x ^{2} - 5}{x ^{2}}

x \to 4 lim (lo g_{2} (x))

\frac{\partial}{\partial x} (x^{2} + 2 x y - y^{2})

\int 1 + 100 x^{2} d x

\frac{1}{2} y^{^{'}} + 2 y = 0

What is the derivative of (x^2+5)/x ?
The derivative of (x^2+5)/x is (x^2-5)/(x^2)
What is the first derivative of (x^2+5)/x ?
The first derivative of (x^2+5)/x is (x^2-5)/(x^2)