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}}

y^{^{'}} + 7 y = 9

\int (8 x ln (x)) d x

x \to \infty lim (3 x + 2)

\frac{d}{d y} (\frac{y}{2})

\int_{0}^{2} x \cdot \frac{1}{2} (2 - x) 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)