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

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Answer 1 · 2016-06-08T08:15:13

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

#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}#