What is the derivative of ((x^2+1)/(2x^2-3x)) ?

The derivative of ((x^2+1)/(2x^2-3x)) is (-3x^2-4x+3)/((2x^2-3x)^2)

What is the first derivative of ((x^2+1)/(2x^2-3x)) ?

The first derivative of ((x^2+1)/(2x^2-3x)) is (-3x^2-4x+3)/((2x^2-3x)^2)

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

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

Solution steps

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

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

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

= \frac{2 x ( 2 x ^{2} - 3 x ) - ( 4 x - 3 ) ( x ^{2} + 1 )}{( 2 x ^{2} - 3 x ) ^{2}}

Expand

2 x (2 x^{2} - 3 x) - (4 x - 3) (x^{2} + 1) : - 3 x^{2} - 4 x + 3

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

f (x) = (9 x^{6} + 8 x^{3})^{4}

\int 5 x^{2} x + 9 d x

f (x) = 9 x + 4 x^{- 1}

\int_{0}^{1} (y^{6} + y^{8}) d y

What is the derivative of ((x^2+1)/(2x^2-3x)) ?
The derivative of ((x^2+1)/(2x^2-3x)) is (-3x^2-4x+3)/((2x^2-3x)^2)
What is the first derivative of ((x^2+1)/(2x^2-3x)) ?
The first derivative of ((x^2+1)/(2x^2-3x)) is (-3x^2-4x+3)/((2x^2-3x)^2)