If f(x)=1-x/2+x find the derivatives of f (using f′(x)=limh⇒0f(x+h)−f(x)h

Step 1The given function is f(x)=1−x2+x.Step 2Obtain the derivative as follows:f′(x)=limh⇒0f(x+h)−f(x)h=limh⇒0(1−(x+h)2+x+h−(1−x2+x)h)=limh⇒0(1−(x)2−h2+x+h−1+x2−xh)=limh⇒0(−h2+hh)=limh⇒0(−h+2h2h)=12

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zagonek34

Answered question

2021-12-10

If f(x)=1-x/2+x find the derivatives of f (using

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

Answer & Explanation

turtletalk75

Beginner2021-12-11Added 29 answers

Step 1
The given function is

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

.
Step 2
Obtain the derivative as follows:

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

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

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

= lim_{h \Rightarrow 0} (\frac{- \frac{h}{2} + h}{h})

= lim_{h \Rightarrow 0} (\frac{- h + 2 h}{2 h})

= \frac{1}{2}

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