What is the derivative of ((4x^2-1/2 x)/((9x+8))) ?

The derivative of ((4x^2-1/2 x)/((9x+8))) is (36x^2+64x-4)/((9x+8)^2)

What is the first derivative of ((4x^2-1/2 x)/((9x+8))) ?

The first derivative of ((4x^2-1/2 x)/((9x+8))) is (36x^2+64x-4)/((9x+8)^2)

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\frac{d}{d x} (\frac{( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 )})

\frac{36 x ^{2} + 64 x - 4}{( 9 x + 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 )})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{2} - \frac{1}{2} x ) ( 9 x + 8 ) - \frac{d}{d x} ( 9 x + 8 ) ( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 ) ^{2}}

\frac{d}{d x} (4 x^{2} - \frac{1}{2} x) = 8 x - \frac{1}{2}

\frac{d}{d x} (9 x + 8) = 9

= \frac{( 8 x - \frac{1}{2} ) ( 9 x + 8 ) - 9 ( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 ) ^{2}}

Simplify

\frac{( 8 x - \frac{1}{2} ) ( 9 x + 8 ) - 9 ( 4 x ^{2} - \frac{1}{2} x )}{( 9 x + 8 ) ^{2}} : \frac{36 x ^{2} + 64 x - 4}{( 9 x + 8 ) ^{2}}

= \frac{36 x ^{2} + 64 x - 4}{( 9 x + 8 ) ^{2}}

\frac{d}{d x} (1.8 x + 2.5)

\int \frac{5 x + 1}{( 2 x + 1 ) ( x - 1 )} d x

\int \frac{x ^{3}}{( x ^{2} + 1 ) ^{3}} d x

\int \frac{1}{1 - z ^{2}} d z

x \to 1 + lim (e^{l n (l n (x))})

What is the derivative of ((4x^2-1/2 x)/((9x+8))) ?
The derivative of ((4x^2-1/2 x)/((9x+8))) is (36x^2+64x-4)/((9x+8)^2)
What is the first derivative of ((4x^2-1/2 x)/((9x+8))) ?
The first derivative of ((4x^2-1/2 x)/((9x+8))) is (36x^2+64x-4)/((9x+8)^2)