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Popular >

derivative of (2+3x/(x^2))

Solution

\frac{d}{d x} (\frac{2 + 3 x}{x ^{2}})

Solution

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

Solution steps

\frac{d}{d x} (\frac{2 + 3 x}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 + 3 x ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( 2 + 3 x )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (2 + 3 x) = 3

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

= \frac{3 x ^{2} - 2 x ( 2 + 3 x )}{( x ^{2} ) ^{2}}

Simplify

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

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

Graph

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Frequently Asked Questions (FAQ)

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