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

The derivative of (x+6/(x-6)) is -(12)/((x-6)^2)

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

The first derivative of (x+6/(x-6)) is -(12)/((x-6)^2)

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

- \frac{12}{( x - 6 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x - 6 ) - 1 \cdot ( x + 6 )}{( x - 6 ) ^{2}} : - \frac{12}{( x - 6 ) ^{2}}

= - \frac{12}{( x - 6 ) ^{2}}

\frac{d}{d x} (7 + 9 x)

x \to - 1.9 lim (2 sin (x))

x \to 1 - lim (\frac{4}{x - 1})

(x - 6) y^{^{'}} + y = x^{2} + 18

\frac{\partial}{\partial y} (10 y^{2} e^{10 x y})

What is the derivative of (x+6/(x-6)) ?
The derivative of (x+6/(x-6)) is -(12)/((x-6)^2)
What is the first derivative of (x+6/(x-6)) ?
The first derivative of (x+6/(x-6)) is -(12)/((x-6)^2)