Use the four step process to find the derivative of f(x) where f'(x) = lim [f(x+h)-f(x)]/h (the lim is h to 0) : f(x) = 1 / 4x-3
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Using the 4 step process you can find f'(x) below:
1) f(x+h) = 1/ (4(x+h)-3) and f(x) = 1 / 4x-3
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neela | Student
f(x) = 1/4x-3
To find the derivative of f(x) = f'(x) defined like Lim h-->0 (f(x+h)-f(x))/h.
Therefore,
f'(x) = lim h-->0 [[1/4(x+h)-3 ]-[1/4x-3]}
=lim h-->0 [1/4(x+h)-1/4x]/h
=lim h-->0 [x-(x+h)]/[4(x+h)(x)h],
lim h-->0 [-h]/[4(x+h)(x)h],h gets cancelled in numerator and denominator.
=Lim h-->0 [-1]/(4x+h)(x) = -1/[4x+0)x] = 1/94x^2)
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