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

The derivative of (4-x^2/(3x-2)) is (-3x^2+4x-12)/((3x-2)^2)

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

The first derivative of (4-x^2/(3x-2)) is (-3x^2+4x-12)/((3x-2)^2)

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

\frac{- 3 x ^{2} + 4 x - 12}{( 3 x - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 - x ^{2} ) ( 3 x - 2 ) - \frac{d}{d x} ( 3 x - 2 ) ( 4 - x ^{2} )}{( 3 x - 2 ) ^{2}}

\frac{d}{d x} (4 - x^{2}) = - 2 x

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

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

Simplify

\frac{( - 2 x ) ( 3 x - 2 ) - 3 ( 4 - x ^{2} )}{( 3 x - 2 ) ^{2}} : \frac{- 3 x ^{2} + 4 x - 12}{( 3 x - 2 ) ^{2}}

= \frac{- 3 x ^{2} + 4 x - 12}{( 3 x - 2 ) ^{2}}

y^{^{'}} = \frac{- 1}{x ^{2}}

n = 0 \sum \infty \frac{1}{5} \cdot (- \frac{2}{3})^{n}

x^{2} + y^{2} = 25, (- 4, 3)

f (x) = \frac{4 x}{x ^{2} + 3}, at x = 1

x \to 0 + lim (cos (\frac{π}{x}))

What is the derivative of (4-x^2/(3x-2)) ?
The derivative of (4-x^2/(3x-2)) is (-3x^2+4x-12)/((3x-2)^2)
What is the first derivative of (4-x^2/(3x-2)) ?
The first derivative of (4-x^2/(3x-2)) is (-3x^2+4x-12)/((3x-2)^2)