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

The derivative of f(x)=(8x+x^2)/((4+x)^2) is (32)/((4+x)^3)

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

The first derivative of f(x)=(8x+x^2)/((4+x)^2) is (32)/((4+x)^3)

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derivative of

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

\frac{32}{( 4 + x ) ^{3}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{( 8 + 2 x ) ( 4 + x ) ^{2} - 2 ( 4 + x ) ( 8 x + x ^{2} )}{( ( 4 + x ) ^{2} ) ^{2}} : \frac{32}{( 4 + x ) ^{3}}

= \frac{32}{( 4 + x ) ^{3}}

\frac{\partial}{\partial L} (- 2 K^{2} + L^{2})

\int_{2}^{4} \frac{1}{( x - 2 ) ^{3}} d x

\int \frac{1}{5 ( x ^{2} + 1 )} d x

\int \frac{9 + 9 x}{1 + x ^{2}} d x

\frac{d y}{d x} = \frac{x ^{2} + 3 y ^{2}}{2 x y}

What is the derivative of f(x)=(8x+x^2)/((4+x)^2) ?
The derivative of f(x)=(8x+x^2)/((4+x)^2) is (32)/((4+x)^3)
What is the first derivative of f(x)=(8x+x^2)/((4+x)^2) ?
The first derivative of f(x)=(8x+x^2)/((4+x)^2) is (32)/((4+x)^3)