How do you find the derivative of g(x)=−2x+1 using the limit definition?

f′(x)=limh→0f(x+h)−f(x)h=limh→0−2x+h+1+2x+1h=limh→0−2(x+1)(x+h+1)(x+1)+2(x+h+1)(x+h+1)(x+1)h=limh→02h(x+h+1)(x+1)h=limh→02(x+h+1)(x+1)=2(x+1)2

"How do you find the derivative of g(x)=−2x+1..." was answered by our community

Mina Whitehead

2022-04-16

How do you find the derivative of

g (x) = - \frac{2}{x + 1}

using the limit definition?

Coupewopmergorlpt

Beginner2022-04-17Added 13 answers

f^{'} (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h}

= lim_{h \to 0} \frac{- \frac{2}{x + h + 1} + \frac{2}{x + 1}}{h}

= lim_{h \to 0} \frac{\frac{- 2 (x + 1)}{(x + h + 1) (x + 1)} + \frac{2 (x + h + 1)}{(x + h + 1) (x + 1)}}{h}

= lim_{h \to 0} \frac{\frac{2 h}{(x + h + 1) (x + 1)}}{h} = lim_{h \to 0} \frac{2}{(x + h + 1) (x + 1)}

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

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