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

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

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

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

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derivative of

f (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 = 0 \sum \infty \frac{1}{n ^{1}}

y^{^{''}} + 8 y^{^{'}} + 15 y = 4

y = \frac{4 x}{x ^{2} - 5}, (3, 3)

\int 4 e^{x} - \frac{5}{x} d x

5 x - x^{2}, 2 x, 0, 3

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