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Popular >

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

Solution

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

Solution

\frac{23}{( 4 x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x - 2) = 5

\frac{d}{d x} (4 x + 3) = 4

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

Expand

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

= \frac{23}{( 4 x + 3 ) ^{2}}

Graph

Popular Examples

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f (x) = arcsec (e^{2 x})

y^{^{'}} + \frac{1}{2} y = 5

limit as x approaches 7-of sqrt(x-7)

x \to 7 - lim (x - 7)

integral of sin(5x)ln(sin(5x))

\int sin (5 x) ln (sin (5 x)) d x

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

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

Frequently Asked Questions (FAQ)

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