What is the derivative of (x^2)/(5(4-x)) ?

The derivative of (x^2)/(5(4-x)) is (8x-x^2)/(5(4-x)^2)

What is the first derivative of (x^2)/(5(4-x)) ?

The first derivative of (x^2)/(5(4-x)) is (8x-x^2)/(5(4-x)^2)

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derivative of

\frac{x ^{2}}{5 ( 4 - x )}

\frac{8 x - x ^{2}}{5 ( 4 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{5 ( 4 - x )})

Take the constant out:

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

= \frac{1}{5} \frac{d}{d x} (\frac{x ^{2}}{4 - x})

Apply the Quotient Rule:

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

= \frac{1}{5} \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( 4 - x ) - \frac{d}{d x} ( 4 - x ) x ^{2}}{( 4 - x ) ^{2}}

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

\frac{d}{d x} (4 - x) = - 1

= \frac{1}{5} \cdot \frac{2 x ( 4 - x ) - ( - 1 ) x ^{2}}{( 4 - x ) ^{2}}

Simplify

\frac{1}{5} \cdot \frac{2 x ( 4 - x ) - ( - 1 ) x ^{2}}{( 4 - x ) ^{2}} : \frac{8 x - x ^{2}}{5 ( 4 - x ) ^{2}}

= \frac{8 x - x ^{2}}{5 ( 4 - x ) ^{2}}

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

\int - x^{2} y^{2} sin (x) + 2 x y^{2} cos (x) d x

(- 10, 9), (- 2, - 5)

{\frac{10}{s ( s + 2 )}}

\frac{d}{d x} (7 (x^{3} - x)^{4})

What is the derivative of (x^2)/(5(4-x)) ?
The derivative of (x^2)/(5(4-x)) is (8x-x^2)/(5(4-x)^2)
What is the first derivative of (x^2)/(5(4-x)) ?
The first derivative of (x^2)/(5(4-x)) is (8x-x^2)/(5(4-x)^2)