What is the derivative of (1-6x/(2+x)) ?

The derivative of (1-6x/(2+x)) is -(13)/((2+x)^2)

What is the first derivative of (1-6x/(2+x)) ?

The first derivative of (1-6x/(2+x)) is -(13)/((2+x)^2)

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\frac{d}{d x} (\frac{1 - 6 x}{2 + x})

- \frac{13}{( 2 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{1 - 6 x}{2 + x})

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (2 + x) = 1

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

Simplify

\frac{( - 6 ) ( 2 + x ) - 1 \cdot ( 1 - 6 x )}{( 2 + x ) ^{2}} : - \frac{13}{( 2 + x ) ^{2}}

= - \frac{13}{( 2 + x ) ^{2}}

(t^{2} + e^{t}) t

\frac{d}{d x} (cos^{2} (x) tan (x))

\frac{d}{d x} (cot (x) d x)

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

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

What is the derivative of (1-6x/(2+x)) ?
The derivative of (1-6x/(2+x)) is -(13)/((2+x)^2)
What is the first derivative of (1-6x/(2+x)) ?
The first derivative of (1-6x/(2+x)) is -(13)/((2+x)^2)