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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int_{- π}^{π} cos^{2} (n x) d x

e^{x^{2}}, 0

\int_{- 1}^{0} x^{3} + 1 d x

18 x - 3 x

f (x) = - 1 - 9 x^{2}, at x = 3

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