(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the definition of a derivitive to find f'(x).

f(x)=1/(1-4X)

2. Relevant equations

Lim as h approaches 0 [f(x+h)-f(x)]/h

3. The attempt at a solution

I know that the answer is supposed to be -1/(1-4X)^{2}but I keep getting 4/(1-4X)^{2}. This is what I have done so far (I hope this isn't too hard to understand):

f'(x)= (1/(1-4(x+h))-(1/(1-4x)))/h

= ((1-4x-(1-4(x+h)))/((1-4(x+h))(1-4x)))/h

= ((1-4x-1+4x+4h)/((1-4(x+h))(1-4x)))/h

*cancel the numerator values*

=(4h)/((1-4(x+h))(1-4x))/h

*divide by 1/h and let h=0*

=4/(1-4(x-0))(1-4x)

=4/(1-4X)^{2}

What am I doing wrong?

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# Homework Help: F'(x) of a fraction

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