Dfferentials. Consider the following function and express the relationship between a small change in x and the corresponding change in y in the form dy=f '(x)dx f(x)= x+4/4-x
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If x increases by a small amount h then y increases by a small amount k. dy/dx approximates to k/h.





8h/((4-x)²-h(4-x)). In the denominator the term h(4-x) is small compared to (4-x)², so we can ignore it.

Therefore k=8h/(4-x)² and k/h=8/(4-x)².

The derivative of f(x)=f'(x)=(4-x+(4+x))/(4-x)²=8/(4-x)². This is the same as k/h=dy/dx.



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