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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\frac{d}{d x} (\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}}

f (x) = 2 x^{2} + 1

\int \frac{8 e ^{2 x}}{e ^{2 x} + 3 e ^{x} + 2} d x

6 cos (x) csc (x^{2})

cos (3 t + 5)

x \to - 2 + lim (2 x + 2 + x)

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)