What is the derivative of (6x+8x^2)/((3+8x)^2) ?

The derivative of (6x+8x^2)/((3+8x)^2) is (18)/((3+8x)^3)

What is the first derivative of (6x+8x^2)/((3+8x)^2) ?

The first derivative of (6x+8x^2)/((3+8x)^2) is (18)/((3+8x)^3)

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derivative of

\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

\frac{18}{( 3 + 8 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 6 x + 8 x ^{2} ) ( 3 + 8 x ) ^{2} - \frac{d}{d x} ( ( 3 + 8 x ) ^{2} ) ( 6 x + 8 x ^{2} )}{( ( 3 + 8 x ) ^{2} ) ^{2}}

\frac{d}{d x} (6 x + 8 x^{2}) = 6 + 16 x

\frac{d}{d x} ((3 + 8 x)^{2}) = 16 (3 + 8 x)

= \frac{( 6 + 16 x ) ( 3 + 8 x ) ^{2} - 16 ( 3 + 8 x ) ( 6 x + 8 x ^{2} )}{( ( 3 + 8 x ) ^{2} ) ^{2}}

Simplify

\frac{( 6 + 16 x ) ( 3 + 8 x ) ^{2} - 16 ( 3 + 8 x ) ( 6 x + 8 x ^{2} )}{( ( 3 + 8 x ) ^{2} ) ^{2}} : \frac{18}{( 3 + 8 x ) ^{3}}

= \frac{18}{( 3 + 8 x ) ^{3}}

\frac{d x}{d t} = - 2 x + t

x, at 4

x \to 0 lim ((1 - 5 x)^{\frac{3}{x}})

x^{3} csc (x)

\frac{d}{d x} (ln ((ln (x))^{2}))

What is the derivative of (6x+8x^2)/((3+8x)^2) ?
The derivative of (6x+8x^2)/((3+8x)^2) is (18)/((3+8x)^3)
What is the first derivative of (6x+8x^2)/((3+8x)^2) ?
The first derivative of (6x+8x^2)/((3+8x)^2) is (18)/((3+8x)^3)