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Popular >

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

Solution

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

Solution

\frac{23}{( 5 x + 4 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

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

= \frac{23}{( 5 x + 4 ) ^{2}}

Popular Examples

integral of (x+6)(x-4)

\int (x + 6) (x - 4) d x

integral of 5/(2x-1)

\int \frac{5}{2 x - 1} d x

integral from 5 to 8 of (x-7)^2

\int_{5}^{8} (x - 7)^{2} d x

(dy)/(dx)= 1/(y^3)

\frac{d y}{d x} = \frac{1}{y ^{3}}

limit as x approaches-2+of (x+1)/(x+2)

x \to - 2 + lim (\frac{x + 1}{x + 2})

Frequently Asked Questions (FAQ)

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