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Popular >

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

Solution

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

Solution

- \frac{8}{( 3 x - 2 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{1 \cdot ( 3 x - 2 ) - 3 ( x + 2 )}{( 3 x - 2 ) ^{2}} : - \frac{8}{( 3 x - 2 ) ^{2}}

= - \frac{8}{( 3 x - 2 ) ^{2}}

Popular Examples

integral of 1/(e^xsqrt(1-e^{-2x))}

\int \frac{1}{e ^{x} 1 - e ^{- 2 x}} d x

integral of x/((x+2)(4x-1))

\int \frac{x}{( x + 2 ) ( 4 x - 1 )} d x

derivative of x^{2.1}

\frac{d}{d x} (x^{2.1})

derivative of ln((sqrt(a^2-x^2)/x))

\frac{d}{d x} (ln (\frac{a ^{2} - x ^{2}}{x}))

derivative of y(X)=-3^X derivative of

y (X) = - 3^{X}

Frequently Asked Questions (FAQ)

What is the derivative of (x+2/(3x-2)) ?
The derivative of (x+2/(3x-2)) is -8/((3x-2)^2)
What is the first derivative of (x+2/(3x-2)) ?
The first derivative of (x+2/(3x-2)) is -8/((3x-2)^2)