What is the derivative of (10x+4x^2/((5+4x)^2)) ?

The derivative of (10x+4x^2/((5+4x)^2)) is (50)/((5+4x)^3)

What is the first derivative of (10x+4x^2/((5+4x)^2)) ?

The first derivative of (10x+4x^2/((5+4x)^2)) is (50)/((5+4x)^3)

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\frac{d}{d x} (\frac{10 x + 4 x ^{2}}{( 5 + 4 x ) ^{2}})

\frac{50}{( 5 + 4 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{10 x + 4 x ^{2}}{( 5 + 4 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 + 4 x ^{2} ) ( 5 + 4 x ) ^{2} - \frac{d}{d x} ( ( 5 + 4 x ) ^{2} ) ( 10 x + 4 x ^{2} )}{( ( 5 + 4 x ) ^{2} ) ^{2}}

\frac{d}{d x} (10 x + 4 x^{2}) = 10 + 8 x

\frac{d}{d x} ((5 + 4 x)^{2}) = 8 (5 + 4 x)

= \frac{( 10 + 8 x ) ( 5 + 4 x ) ^{2} - 8 ( 5 + 4 x ) ( 10 x + 4 x ^{2} )}{( ( 5 + 4 x ) ^{2} ) ^{2}}

Simplify

\frac{( 10 + 8 x ) ( 5 + 4 x ) ^{2} - 8 ( 5 + 4 x ) ( 10 x + 4 x ^{2} )}{( ( 5 + 4 x ) ^{2} ) ^{2}} : \frac{50}{( 5 + 4 x ) ^{3}}

= \frac{50}{( 5 + 4 x ) ^{3}}

\frac{d}{d x} ((2 x + 5)^{3} \cdot (3 x - 1)^{4})

\int (- 2^{3 - 2 x}) d x

\int \frac{y}{x} d x

\frac{\partial}{\partial y} (cos (x) + sin (y))

f (x) = 3 6 x + 8

What is the derivative of (10x+4x^2/((5+4x)^2)) ?
The derivative of (10x+4x^2/((5+4x)^2)) is (50)/((5+4x)^3)
What is the first derivative of (10x+4x^2/((5+4x)^2)) ?
The first derivative of (10x+4x^2/((5+4x)^2)) is (50)/((5+4x)^3)