What is the derivative of (3x-2/(x^2)) ?

The derivative of (3x-2/(x^2)) is (-3x+4)/(x^3)

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\int (x^{5} - 9 + \frac{6}{x ^{7}}) d x

\frac{d}{d x} (y + x) + x + y + 1 = 0

\int \frac{1}{- x ^{2} + 2 x + 8} d x

\frac{\partial}{\partial x} (2 x y + y cos (x))

e^{8 x} - e^{2 x}, x = 1

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