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

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

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

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

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derivative of

y = \frac{( x + 2 ) ^{2}}{x}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (\frac{1}{x ^{4}})

\frac{( e ^{x} - 1 )}{x}

y = x^{3} - x^{2} + x - 1

\frac{4}{( x - 1 )}

\frac{8}{( ( x - 2 ) ^{\frac{1}{2}} )}

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