Question

Differentiate the following by the first principle : f(x) = 2x + 3

Answer 1

It's not differential equation...
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\[f(x) = 2x + 3\]\[f'(x) = lim_{h\rightarrow 0}\frac{2(x+h) +3 - (2x+3)}{h}\]
Can you simplify 2(x+h) +3 - (2x+3)?

Answer 2

yes

Answer 3

What do you get?

Answer 4

the ans is 2

Answer 5

I know the answer is 2. I was asking what have you got after simplifying 2(x+h) +3 - (2x+3).

Answer 6

ans iz 2

Answer 7

f(x)=2x + 2h +3 - 2x-3/h
=2h/h
=2
\[\prime(x)\]

Answer 8

Almost correct. It's just the problem of notation.
f(x) = 2x+3
\[f'(x)\]\[ = lim_{h\rightarrow 0}\frac{2(x+h) +3 - (2x+3)}{h}\]\[= lim_{h\rightarrow 0}\frac{2x+2h +3 - (2x+3)}{h}\]\[=lim_{h\rightarrow 0}\frac{2h}{h}\]\[=2\]