What is the derivative of (2x+8x^2/((1+8x)^2)) ?

The derivative of (2x+8x^2/((1+8x)^2)) is 2/((1+8x)^3)

What is the first derivative of (2x+8x^2/((1+8x)^2)) ?

The first derivative of (2x+8x^2/((1+8x)^2)) is 2/((1+8x)^3)

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\frac{d}{d x} (\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}})

\frac{2}{( 1 + 8 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 x + 8 x ^{2}}{( 1 + 8 x ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 8 x ^{2} ) ( 1 + 8 x ) ^{2} - \frac{d}{d x} ( ( 1 + 8 x ) ^{2} ) ( 2 x + 8 x ^{2} )}{( ( 1 + 8 x ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((1 + 8 x)^{2}) = 16 (1 + 8 x)

= \frac{( 2 + 16 x ) ( 1 + 8 x ) ^{2} - 16 ( 1 + 8 x ) ( 2 x + 8 x ^{2} )}{( ( 1 + 8 x ) ^{2} ) ^{2}}

Simplify

\frac{( 2 + 16 x ) ( 1 + 8 x ) ^{2} - 16 ( 1 + 8 x ) ( 2 x + 8 x ^{2} )}{( ( 1 + 8 x ) ^{2} ) ^{2}} : \frac{2}{( 1 + 8 x ) ^{3}}

= \frac{2}{( 1 + 8 x ) ^{3}}

n = 1 \sum \infty \frac{5 n}{4 n + 3}

h \to 3 lim (\frac{( - 3 h + 5 - 5 )}{h})

x \to 3 + lim (ln (x - 3))

x \to - 3 lim (x - 3)

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

What is the derivative of (2x+8x^2/((1+8x)^2)) ?
The derivative of (2x+8x^2/((1+8x)^2)) is 2/((1+8x)^3)
What is the first derivative of (2x+8x^2/((1+8x)^2)) ?
The first derivative of (2x+8x^2/((1+8x)^2)) is 2/((1+8x)^3)