What is the derivative of f(x)=(10x+8x^2)/((5+8x)^2) ?

The derivative of f(x)=(10x+8x^2)/((5+8x)^2) is (50)/((5+8x)^3)

What is the first derivative of f(x)=(10x+8x^2)/((5+8x)^2) ?

The first derivative of f(x)=(10x+8x^2)/((5+8x)^2) is (50)/((5+8x)^3)

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derivative of

f (x) = \frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}}

\frac{50}{( 5 + 8 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{10 x + 8 x ^{2}}{( 5 + 8 x ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 10 x + 8 x ^{2} ) ( 5 + 8 x ) ^{2} - \frac{d}{d x} ( ( 5 + 8 x ) ^{2} ) ( 10 x + 8 x ^{2} )}{( ( 5 + 8 x ) ^{2} ) ^{2}}

\frac{d}{d x} (10 x + 8 x^{2}) = 10 + 16 x

\frac{d}{d x} ((5 + 8 x)^{2}) = 16 (5 + 8 x)

= \frac{( 10 + 16 x ) ( 5 + 8 x ) ^{2} - 16 ( 5 + 8 x ) ( 10 x + 8 x ^{2} )}{( ( 5 + 8 x ) ^{2} ) ^{2}}

Simplify

\frac{( 10 + 16 x ) ( 5 + 8 x ) ^{2} - 16 ( 5 + 8 x ) ( 10 x + 8 x ^{2} )}{( ( 5 + 8 x ) ^{2} ) ^{2}} : \frac{50}{( 5 + 8 x ) ^{3}}

= \frac{50}{( 5 + 8 x ) ^{3}}

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What is the derivative of f(x)=(10x+8x^2)/((5+8x)^2) ?
The derivative of f(x)=(10x+8x^2)/((5+8x)^2) is (50)/((5+8x)^3)
What is the first derivative of f(x)=(10x+8x^2)/((5+8x)^2) ?
The first derivative of f(x)=(10x+8x^2)/((5+8x)^2) is (50)/((5+8x)^3)