find the derivative using limit definition
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Derivative of (x²-4)(x²-5) from first principles.

Let y=f(x).

We consider a small increment h in x which creates a corresponding increase k in y.


y+k=(x²+2xh-4)(x²+2xh-5). h² is ignored as insignificantly small.


To find k, we subtract f(x):




In the limit as h,k→0, h/k=dy/dx=4x³-18x. This is the derivative of f(x).

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