What is the derivative of (4x-x^2/(6-x)) ?

The derivative of (4x-x^2/(6-x)) is (x^2-12x+24)/((6-x)^2)

What is the first derivative of (4x-x^2/(6-x)) ?

The first derivative of (4x-x^2/(6-x)) is (x^2-12x+24)/((6-x)^2)

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\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})

\frac{x ^{2} - 12 x + 24}{( 6 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x - x ^{2}}{6 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x - x ^{2} ) ( 6 - x ) - \frac{d}{d x} ( 6 - x ) ( 4 x - x ^{2} )}{( 6 - x ) ^{2}}

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

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

= \frac{( 4 - 2 x ) ( 6 - x ) - ( - 1 ) ( 4 x - x ^{2} )}{( 6 - x ) ^{2}}

Simplify

\frac{( 4 - 2 x ) ( 6 - x ) - ( - 1 ) ( 4 x - x ^{2} )}{( 6 - x ) ^{2}} : \frac{x ^{2} - 12 x + 24}{( 6 - x ) ^{2}}

= \frac{x ^{2} - 12 x + 24}{( 6 - x ) ^{2}}

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

\frac{d y}{d x} = y^{\frac{1}{2}}

\int \frac{72}{1 - cos ( 8 x )} d x

e^{- x^{4}}

\int \frac{1}{( 8 x + 9 ) ^{2}} d x

What is the derivative of (4x-x^2/(6-x)) ?
The derivative of (4x-x^2/(6-x)) is (x^2-12x+24)/((6-x)^2)
What is the first derivative of (4x-x^2/(6-x)) ?
The first derivative of (4x-x^2/(6-x)) is (x^2-12x+24)/((6-x)^2)