Solved: "Differentiate f(x)=2x-3 using first principal?"

Dexter Odom

Answered question

2022-03-28

Differentiate f(x)=2x-3 using first principal?

Answer & Explanation

armejantm925

Beginner2022-03-29Added 20 answers

For a function f(x), its derivative using first principal is given by

\frac{d f}{d x} = L t_{h \to 0} \frac{f (x + h) - f (x)}{h}

Here we have f(x)=2x-3,
hence f(x+h)=2(x+h)-3=2x+2h-3
and f(x+h)=f(x)=2h
and

\frac{d f}{d x} = L t_{h \to 0} \frac{f (x + h) - f (x)}{h}

= L t_{h \to 0} \frac{2 h}{h}

= L t_{h \to 0} 2

Dixie Reed

Beginner2022-03-30Added 15 answers

Explanation:
differentiating from first principles
$f^{'} (x) = lim_{h \to 0} \frac{f (x + h) - f (x)}{h}$
$= lim_{h \to 0} \frac{2 (x + h) - 3 - 2 x + 3}{h}$
$= lim_{h \to 0} \frac{2 x + 2 h - 2 x}{h}$
$= \lim_{h \to 0} \frac{2 h}{h} = 2$
Result:
f'(x)=2

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