Question

find derivation of 2x+3 from 1st principle..​

Answer 1

Let, f(x) = 2x + 3

Now,

lim h→0 f(x+h)-f(x) / h

= lim h→0 2(x+h)-2x / h

= lim h→0 {2(x+h)-2x}{2(x+h)+2x} / h{2(x+h) + 2x}

= lim h→0 4(x+h)²-4x² / h{2(x+h) + 2x}

(Simplify it)

= lim h→0 (4h² + 8xh) / h{2(x+h) + 2x}

= lim h→0 h(4h+8x) / h{2(x+h) + 2x}

= 4(0) + 8x / 2(x+0) + 2x

(Put value h=0)

= 8x / 4x = 2

This is your answer

Hope It Helps:)

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