What is the derivative of 8ln((5x+7)/(3x^2-6x)) ?

The derivative of 8ln((5x+7)/(3x^2-6x)) is -(8(5x^2+14x-14))/(x(5x+7)(x-2))

What is the first derivative of 8ln((5x+7)/(3x^2-6x)) ?

The first derivative of 8ln((5x+7)/(3x^2-6x)) is -(8(5x^2+14x-14))/(x(5x+7)(x-2))

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derivative of

8 ln (\frac{5 x + 7}{3 x ^{2} - 6 x})

- \frac{8 ( 5 x ^{2} + 14 x - 14 )}{x ( 5 x + 7 ) ( x - 2 )}

Solution steps

\frac{d}{d x} (8 ln (\frac{5 x + 7}{3 x ^{2} - 6 x}))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 8 \frac{d}{d x} (ln (\frac{5 x + 7}{3 x ^{2} - 6 x}))

Apply the chain rule:

\frac{1}{\frac{5 x + 7}{3 x ^{2} - 6 x}} \frac{d}{d x} (\frac{5 x + 7}{3 x ^{2} - 6 x})

= \frac{1}{\frac{5 x + 7}{3 x ^{2} - 6 x}} \frac{d}{d x} (\frac{5 x + 7}{3 x ^{2} - 6 x})

\frac{d}{d x} (\frac{5 x + 7}{3 x ^{2} - 6 x}) = - \frac{5 x ^{2} + 14 x - 14}{3 x ^{2} ( x - 2 ) ^{2}}

= 8 \cdot \frac{1}{\frac{5 x + 7}{3 x ^{2} - 6 x}} (- \frac{5 x ^{2} + 14 x - 14}{3 x ^{2} ( x - 2 ) ^{2}})

Simplify

8 \cdot \frac{1}{\frac{5 x + 7}{3 x ^{2} - 6 x}} (- \frac{5 x ^{2} + 14 x - 14}{3 x ^{2} ( x - 2 ) ^{2}}) : - \frac{8 ( 5 x ^{2} + 14 x - 14 )}{x ( 5 x + 7 ) ( x - 2 )}

= - \frac{8 ( 5 x ^{2} + 14 x - 14 )}{x ( 5 x + 7 ) ( x - 2 )}

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

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

y y^{^{'}} = x^{2}

\int a^{x} d x

x \to 1 lim (x^{2} + 2 x)

What is the derivative of 8ln((5x+7)/(3x^2-6x)) ?
The derivative of 8ln((5x+7)/(3x^2-6x)) is -(8(5x^2+14x-14))/(x(5x+7)(x-2))
What is the first derivative of 8ln((5x+7)/(3x^2-6x)) ?
The first derivative of 8ln((5x+7)/(3x^2-6x)) is -(8(5x^2+14x-14))/(x(5x+7)(x-2))