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Question

Find the derivative of 2x+33x+2 by first principle.

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Solution

Let f(x) = 2x+33x+2

Then, f(x+h)=2(x+h)+33(x+h)+2

f(x)=limh02(x+h)+33(x+h)+22x+33x+2h

=limh0(2x+3+2h)(3x+2)(2x+3)(3x+2+3h)h(3x+2)(3x+2+3h)

=limh0(2x+3)(3x+2)+2h(3x+2)(2x+3)(3x+2)3h(2x+3)h(3x+2)(3x+2+3h)

=limh0h(6x+46x9)h(3x+2)(3x+2+3h)f(x)=limh05(3x+2)(3x+2+3h)

=5(3x+2)2


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