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Popular >

derivative of (4x-5/(3x+2))

Solution

\frac{d}{d x} (\frac{4 x - 5}{3 x + 2})

Solution

\frac{23}{( 3 x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - 5}{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 - 5 ) ( 3 x + 2 ) - \frac{d}{d x} ( 3 x + 2 ) ( 4 x - 5 )}{( 3 x + 2 ) ^{2}}

\frac{d}{d x} (4 x - 5) = 4

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

= \frac{4 ( 3 x + 2 ) - 3 ( 4 x - 5 )}{( 3 x + 2 ) ^{2}}

Expand

4 (3 x + 2) - 3 (4 x - 5) : 23

= \frac{23}{( 3 x + 2 ) ^{2}}

Popular Examples

(\partial)/(\partial x)(e^{-3x^2-5y^2})

\frac{\partial}{\partial x} (e^{- 3 x^{2} - 5 y^{2}})

integral of (-2ln(x))/(x^2)

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

integral of (e^{-x}(3-3xln(x)))/(2x)

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

integral of 1/(3-(x-2)^2)

\int \frac{1}{3 - ( x - 2 ) ^{2}} d x

integral of 4-|x|

\int 4 - ∣ x ∣ d x

Frequently Asked Questions (FAQ)

What is the derivative of (4x-5/(3x+2)) ?
The derivative of (4x-5/(3x+2)) is (23)/((3x+2)^2)
What is the first derivative of (4x-5/(3x+2)) ?
The first derivative of (4x-5/(3x+2)) is (23)/((3x+2)^2)