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}}

f (x) = - cot (x) csc (x)

f (x) = x (ln (x)) - x

f (x) = \frac{x ^{2} - 3 x}{2 x + 1}

\int \frac{( 7 x ^{2} + x + 7 )}{( x ^{2} + 1 ) ^{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)