What is the derivative of f(x)=(x^2)/((4+x)) ?

The derivative of f(x)=(x^2)/((4+x)) is (8x+x^2)/((4+x)^2)

What is the first derivative of f(x)=(x^2)/((4+x)) ?

The first derivative of f(x)=(x^2)/((4+x)) is (8x+x^2)/((4+x)^2)

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derivative of

f (x) = \frac{x ^{2}}{( 4 + x )}

\frac{8 x + x ^{2}}{( 4 + x ) ^{2}}

Solution steps

\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{\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{2 x ( 4 + x ) - 1 \cdot x ^{2}}{( 4 + x ) ^{2}}

Simplify

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

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

- 9 x^{\frac{1}{3}} + 5, at x = 27

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

\int + (x^{2} - 1) d x

\int π^{2} d x

What is the derivative of f(x)=(x^2)/((4+x)) ?
The derivative of f(x)=(x^2)/((4+x)) is (8x+x^2)/((4+x)^2)
What is the first derivative of f(x)=(x^2)/((4+x)) ?
The first derivative of f(x)=(x^2)/((4+x)) is (8x+x^2)/((4+x)^2)