What is the derivative of f(x)=(4x-3)/(5x^2+3x) ?

The derivative of f(x)=(4x-3)/(5x^2+3x) is (-20x^2+30x+9)/((5x^2+3x)^2)

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

The first derivative of f(x)=(4x-3)/(5x^2+3x) is (-20x^2+30x+9)/((5x^2+3x)^2)

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derivative of

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

\frac{- 20 x ^{2} + 30 x + 9}{( 5 x ^{2} + 3 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (5 x^{2} + 3 x) = 10 x + 3

= \frac{4 ( 5 x ^{2} + 3 x ) - ( 10 x + 3 ) ( 4 x - 3 )}{( 5 x ^{2} + 3 x ) ^{2}}

Expand

4 (5 x^{2} + 3 x) - (10 x + 3) (4 x - 3) : - 20 x^{2} + 30 x + 9

= \frac{- 20 x ^{2} + 30 x + 9}{( 5 x ^{2} + 3 x ) ^{2}}

\int x sin^{3} (x) d x

\int x^{2} arctan (x) d x

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

\frac{d ^{3}}{d x ^{3}} (\frac{7}{x ^{2}})

\frac{\partial}{\partial x} (a^{x})

What is the derivative of f(x)=(4x-3)/(5x^2+3x) ?
The derivative of f(x)=(4x-3)/(5x^2+3x) is (-20x^2+30x+9)/((5x^2+3x)^2)
What is the first derivative of f(x)=(4x-3)/(5x^2+3x) ?
The first derivative of f(x)=(4x-3)/(5x^2+3x) is (-20x^2+30x+9)/((5x^2+3x)^2)