What is the derivative of (8x^2+18x)/((9+8x)^2) ?

The derivative of (8x^2+18x)/((9+8x)^2) is (162)/((9+8x)^3)

What is the first derivative of (8x^2+18x)/((9+8x)^2) ?

The first derivative of (8x^2+18x)/((9+8x)^2) is (162)/((9+8x)^3)

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derivative of

\frac{8 x ^{2} + 18 x}{( 9 + 8 x ) ^{2}}

\frac{162}{( 9 + 8 x ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{8 x ^{2} + 18 x}{( 9 + 8 x ) ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{2} + 18 x ) ( 9 + 8 x ) ^{2} - \frac{d}{d x} ( ( 9 + 8 x ) ^{2} ) ( 8 x ^{2} + 18 x )}{( ( 9 + 8 x ) ^{2} ) ^{2}}

\frac{d}{d x} (8 x^{2} + 18 x) = 16 x + 18

\frac{d}{d x} ((9 + 8 x)^{2}) = 16 (9 + 8 x)

= \frac{( 16 x + 18 ) ( 9 + 8 x ) ^{2} - 16 ( 9 + 8 x ) ( 8 x ^{2} + 18 x )}{( ( 9 + 8 x ) ^{2} ) ^{2}}

Simplify

\frac{( 16 x + 18 ) ( 9 + 8 x ) ^{2} - 16 ( 9 + 8 x ) ( 8 x ^{2} + 18 x )}{( ( 9 + 8 x ) ^{2} ) ^{2}} : \frac{162}{( 9 + 8 x ) ^{3}}

= \frac{162}{( 9 + 8 x ) ^{3}}

x^{\frac{1}{6}}

\frac{d}{d x} (- x^{2} + 13 x - 22)

\int e^{t - s t}

g (x) = 10 x e^{3 - x^{2}}

7 t \cdot y^{^{'}} - 5 y = t

What is the derivative of (8x^2+18x)/((9+8x)^2) ?
The derivative of (8x^2+18x)/((9+8x)^2) is (162)/((9+8x)^3)
What is the first derivative of (8x^2+18x)/((9+8x)^2) ?
The first derivative of (8x^2+18x)/((9+8x)^2) is (162)/((9+8x)^3)