What is the derivative of f(x)=(x+6)/(x-4) ?

The derivative of f(x)=(x+6)/(x-4) is -(10)/((x-4)^2)

What is the first derivative of f(x)=(x+6)/(x-4) ?

The first derivative of f(x)=(x+6)/(x-4) is -(10)/((x-4)^2)

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derivative of

f (x) = \frac{x + 6}{x - 4}

- \frac{10}{( x - 4 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x + 6}{x - 4})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 6 ) ( x - 4 ) - \frac{d}{d x} ( x - 4 ) ( x + 6 )}{( x - 4 ) ^{2}}

\frac{d}{d x} (x + 6) = 1

\frac{d}{d x} (x - 4) = 1

= \frac{1 \cdot ( x - 4 ) - 1 \cdot ( x + 6 )}{( x - 4 ) ^{2}}

Simplify

\frac{1 \cdot ( x - 4 ) - 1 \cdot ( x + 6 )}{( x - 4 ) ^{2}} : - \frac{10}{( x - 4 ) ^{2}}

= - \frac{10}{( x - 4 ) ^{2}}

1 + x

y = (4 x - 1)^{2}

\frac{d}{d x} ((3 x + 4) (- 3 + 2 x))

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

\frac{d}{d x} (\frac{2}{( x - 1 ) ^{2}})

What is the derivative of f(x)=(x+6)/(x-4) ?
The derivative of f(x)=(x+6)/(x-4) is -(10)/((x-4)^2)
What is the first derivative of f(x)=(x+6)/(x-4) ?
The first derivative of f(x)=(x+6)/(x-4) is -(10)/((x-4)^2)