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

The derivative of g(x)=(6x^2)/(2-x) is (6(4x-x^2))/((2-x)^2)

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

The first derivative of g(x)=(6x^2)/(2-x) is (6(4x-x^2))/((2-x)^2)

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derivative of

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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