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Popular >

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

Solution

derivative of

\frac{3 x + 2}{3 x - 2}

Solution

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

Solution steps

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

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

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

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

Simplify

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

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

Popular Examples

derivative of e^{(x^2/2})

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

(\partial)/(\partial x)(5/(x^2+y^2))

\frac{\partial}{\partial x} (\frac{5}{x ^{2} + y ^{2}})

integral from 0 to pi/2 of e^tcos(3t)

\int_{0}^{\frac{π}{2}} e^{t} cos (3 t) d t

derivative of 3arccos(x/8)

\frac{d}{d x} (3 arccos (\frac{x}{8}))

(dy)/(dx)=3+sqrt(y-3x+2)

\frac{d y}{d x} = 3 + y - 3 x + 2

Frequently Asked Questions (FAQ)

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