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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

x^{3} y^{3} - y = x

\frac{d}{d x} (sin (x) + cos (y))

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

\frac{\partial}{\partial x} (x e^{4 y} sin (3 z))

\int \frac{2}{x ^{2} + 10 x + 29} d x

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