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

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

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

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

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\frac{d}{d 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 sec^{5} (\frac{θ}{2}) d θ

t \to 0 lim (\frac{3 e ^{t} - 3}{t})

\frac{\partial}{\partial x} (sin (5 x y + 8 yz + 9 x z))

\int \frac{1}{x ^{2} + π ^{2}} d x

\frac{\partial}{\partial x} (3^{s i n (3 x)})

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