What is the derivative of ((5x-3)/((4x-3/x))) ?

The derivative of ((5x-3)/((4x-3/x))) is (-30x+9+12x^2)/((4x^2-3)^2)

What is the first derivative of ((5x-3)/((4x-3/x))) ?

The first derivative of ((5x-3)/((4x-3/x))) is (-30x+9+12x^2)/((4x^2-3)^2)

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

\frac{- 30 x + 9 + 12 x ^{2}}{( 4 x ^{2} - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x - 3) = 5

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

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

Simplify

\frac{5 ( 4 x - \frac{3}{x} ) - ( 4 + \frac{3}{x ^{2}} ) ( 5 x - 3 )}{( 4 x - \frac{3}{x} ) ^{2}} : \frac{- 30 x + 9 + 12 x ^{2}}{( 4 x ^{2} - 3 ) ^{2}}

= \frac{- 30 x + 9 + 12 x ^{2}}{( 4 x ^{2} - 3 ) ^{2}}

\frac{\partial}{\partial x} (y (- 14 x - 4 y + 1))

\int x (x^{2} + 3)^{2} d x

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

2 x + 3 y + (6 x + 9 y - 3) y^{^{'}} = 0

f (x) = cos (x^{2}) - 2 x^{2} sin (x^{2})

What is the derivative of ((5x-3)/((4x-3/x))) ?
The derivative of ((5x-3)/((4x-3/x))) is (-30x+9+12x^2)/((4x^2-3)^2)
What is the first derivative of ((5x-3)/((4x-3/x))) ?
The first derivative of ((5x-3)/((4x-3/x))) is (-30x+9+12x^2)/((4x^2-3)^2)