How do you differentiate $f (x) = - \frac{1}{2 x - 7}$ $f(x)= -1 / (2x-7 )$ using the quotient rule?

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Answer 1 · 2016-06-08T08:15:13

$\frac{d}{d x} (- \frac{1}{2 x - 7}) = \frac{2}{{(2 x - 7)}^{2}}$ $frac{d}{dx}(-frac{1}{2x-7})=frac{2}{(2x-7)^2}$

$\frac{d}{d x} (- \frac{1}{2 x - 7})$ $frac{d}{dx}(-frac{1}{2x-7})$

Taking the constant out,

$(acdot f)^'=acdot f^'$

$=-frac{d}{dx}(frac{1}{2x-7})$

$=-frac{d}{dx}((2x-7)^{-1})$

$frac{df(u)}{dx}=frac{df}{du}cdot frac{du}{dx}$

$Let,2x-7=u$

$=-frac{d}{du}(u^{-1})frac{d}{dx}(2x-7)$

WE know,

$frac{d}{du}(u^{-1})=-frac{1}{u^2}$

$frac{d}{dx}(2x-7)=2$

$=-(-frac{1}{u^2})2$

Substitute back $=-(-frac{1}{u^2})$
$=-(-frac{1}{(2x-7)^2})2$

$=-(-frac{1}{(2x-7)^2})2$

Simplify,
$frac{2}{(2x-7)^2}$

How do you differentiate f(x)= -1 / (2x-7 )f(x)=−12x−7f(x)= -1 / (2x-7 ) using the quotient rule?