What is the derivative of f(x)=((8x+7)/(9x^2+6)) ?

The derivative of f(x)=((8x+7)/(9x^2+6)) is -(2(12x^2+21x-8))/(3(3x^2+2)^2)

What is the first derivative of f(x)=((8x+7)/(9x^2+6)) ?

The first derivative of f(x)=((8x+7)/(9x^2+6)) is -(2(12x^2+21x-8))/(3(3x^2+2)^2)

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derivative of

f (x) = (\frac{8 x + 7}{9 x ^{2} + 6})

- \frac{2 ( 12 x ^{2} + 21 x - 8 )}{3 ( 3 x ^{2} + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x + 7}{9 x ^{2} + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x + 7 ) ( 9 x ^{2} + 6 ) - \frac{d}{d x} ( 9 x ^{2} + 6 ) ( 8 x + 7 )}{( 9 x ^{2} + 6 ) ^{2}}

\frac{d}{d x} (8 x + 7) = 8

\frac{d}{d x} (9 x^{2} + 6) = 18 x

= \frac{8 ( 9 x ^{2} + 6 ) - 18 x ( 8 x + 7 )}{( 9 x ^{2} + 6 ) ^{2}}

Simplify

\frac{8 ( 9 x ^{2} + 6 ) - 18 x ( 8 x + 7 )}{( 9 x ^{2} + 6 ) ^{2}} : - \frac{2 ( 12 x ^{2} + 21 x - 8 )}{3 ( 3 x ^{2} + 2 ) ^{2}}

= - \frac{2 ( 12 x ^{2} + 21 x - 8 )}{3 ( 3 x ^{2} + 2 ) ^{2}}

y = cos (x), y = sin (x)

7 e^{x}, 7 x e^{x^{2}}, [0, 1]

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

n = 1 \sum \infty \frac{5}{2 ^{n - 1}}

\frac{\partial}{\partial x} (\frac{x - z}{y + z})

What is the derivative of f(x)=((8x+7)/(9x^2+6)) ?
The derivative of f(x)=((8x+7)/(9x^2+6)) is -(2(12x^2+21x-8))/(3(3x^2+2)^2)
What is the first derivative of f(x)=((8x+7)/(9x^2+6)) ?
The first derivative of f(x)=((8x+7)/(9x^2+6)) is -(2(12x^2+21x-8))/(3(3x^2+2)^2)