3x2+4 by first principle

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Please find below the solution to the asked query:

We have:fx=3x2+4fx+h=3x+h2+4By first principle of differentiation, we get:f'x=limh0 fx+h-fxh=limh0 3x+h2+4-3x2+4h=limh0 3x+h2+4-3x2-4h=limh0 3x+h2-3x2h=limh0 3x+h2-x2h=3limh0x+h2-x2h=3limh0x+h-xx+h+xh  a2-b2=a+ba-b=3limh0h2x+hh=3limh02x+hApplying limit we get:f'x=3×2x+0=3×2xf'x=6
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