What is the derivative of (8.7x+0.2/(x^2-4.5x+7.5)) ?

The derivative of (8.7x+0.2/(x^2-4.5x+7.5)) is (-8.7x^2-0.4x+66.15)/((x^2-4.5x+7.5)^2)

What is the first derivative of (8.7x+0.2/(x^2-4.5x+7.5)) ?

The first derivative of (8.7x+0.2/(x^2-4.5x+7.5)) is (-8.7x^2-0.4x+66.15)/((x^2-4.5x+7.5)^2)

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\frac{d}{d x} (\frac{8.7 x + 0.2}{x ^{2} - 4.5 x + 7.5})

\frac{- 8.7 x ^{2} - 0.4 x + 66.15}{( x ^{2} - 4.5 x + 7.5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{8.7 x + 0.2}{x ^{2} - 4.5 x + 7.5})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8.7 x + 0.2 ) ( x ^{2} - 4.5 x + 7.5 ) - \frac{d}{d x} ( x ^{2} - 4.5 x + 7.5 ) ( 8.7 x + 0.2 )}{( x ^{2} - 4.5 x + 7.5 ) ^{2}}

\frac{d}{d x} (8.7 x + 0.2) = 8.7

\frac{d}{d x} (x^{2} - 4.5 x + 7.5) = 2 x - 4.5

= \frac{8.7 ( x ^{2} - 4.5 x + 7.5 ) - ( 2 x - 4.5 ) ( 8.7 x + 0.2 )}{( x ^{2} - 4.5 x + 7.5 ) ^{2}}

Expand

8.7 (x^{2} - 4.5 x + 7.5) - (2 x - 4.5) (8.7 x + 0.2) : - 8.7 x^{2} - 0.4 x + 66.15

= \frac{- 8.7 x ^{2} - 0.4 x + 66.15}{( x ^{2} - 4.5 x + 7.5 ) ^{2}}

x \to 0 + lim (\frac{ln ( x )}{\frac{1}{x}})

f (x) = x^{3} - 3 x - 5, at x = 1

\frac{\partial}{\partial x} (ln (x + 6 y + 8 z))

\frac{d y}{d x} = - \frac{2}{x ^{3}} + 2 e^{2 x - 2}

What is the derivative of (8.7x+0.2/(x^2-4.5x+7.5)) ?
The derivative of (8.7x+0.2/(x^2-4.5x+7.5)) is (-8.7x^2-0.4x+66.15)/((x^2-4.5x+7.5)^2)
What is the first derivative of (8.7x+0.2/(x^2-4.5x+7.5)) ?
The first derivative of (8.7x+0.2/(x^2-4.5x+7.5)) is (-8.7x^2-0.4x+66.15)/((x^2-4.5x+7.5)^2)