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}}

\int x \cdot cos (7 x) d x

\frac{d y}{d x}, x + y + x y = 21

\int a^{2} + x^{2} d x

\int \frac{1 - x + 1}{1 + x + 1} d x

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)