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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Popular >

\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}}

\int (2 x + 3) d x

\frac{\partial}{\partial x} (x y^{2} + 2 x^{2} z)

\int cos (x) + sin (x) d x

\int \frac{x ^{4} - 5 x ^{3} + 7 x}{x} d x

x \to 6 lim (\frac{g ( x )}{f ( x )})

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)