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Popular Calculus >

derivative of y=(x+2)/(x^2)

Solution

derivative of

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

Solution

\frac{- x - 4}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 2) = 1

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

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

Simplify

\frac{1 \cdot x ^{2} - 2 x ( x + 2 )}{( x ^{2} ) ^{2}} : \frac{- x - 4}{x ^{3}}

= \frac{- x - 4}{x ^{3}}

Graph

Popular Examples

derivative of 1/((s+3)^2)

d er i v a t i v e \frac{1}{( s + 3 ) ^{2}}

derivative of 2x^3-24x^1-35

d er i v a t i v e 2 x^{3} - 24 x^{1} - 35

derivative of 4x^3+5

d er i v a t i v e 4 x^{3} + 5

derivative of (x+1)^3*(5-x)

d er i v a t i v e (x + 1)^{3} \cdot (5 - x)

derivative of 1/((5+x))

d er i v a t i v e \frac{1}{( 5 + x )}

Frequently Asked Questions (FAQ)

What is the derivative of y=(x+2)/(x^2) ?
The derivative of y=(x+2)/(x^2) is (-x-4)/(x^3)
What is the first derivative of y=(x+2)/(x^2) ?
The first derivative of y=(x+2)/(x^2) is (-x-4)/(x^3)