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

The derivative of (1-3x^2/(1-2x)) is (6x^2-6x+2)/((1-2x)^2)

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

The first derivative of (1-3x^2/(1-2x)) is (6x^2-6x+2)/((1-2x)^2)

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

\frac{6 x ^{2} - 6 x + 2}{( 1 - 2 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 - 3 x^{2}) = - 6 x

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

= \frac{( - 6 x ) ( 1 - 2 x ) - ( - 2 ) ( 1 - 3 x ^{2} )}{( 1 - 2 x ) ^{2}}

Simplify

\frac{( - 6 x ) ( 1 - 2 x ) - ( - 2 ) ( 1 - 3 x ^{2} )}{( 1 - 2 x ) ^{2}} : \frac{6 x ^{2} - 6 x + 2}{( 1 - 2 x ) ^{2}}

= \frac{6 x ^{2} - 6 x + 2}{( 1 - 2 x ) ^{2}}

\frac{d}{d x} (9 x + 5)

x \to 5 - lim (\frac{1}{( x - 5 ) ^{2}})

10

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

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

What is the derivative of (1-3x^2/(1-2x)) ?
The derivative of (1-3x^2/(1-2x)) is (6x^2-6x+2)/((1-2x)^2)
What is the first derivative of (1-3x^2/(1-2x)) ?
The first derivative of (1-3x^2/(1-2x)) is (6x^2-6x+2)/((1-2x)^2)