u-substitution for integration

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With Leibniz notation, there is a cool trick where if du/dx = g'(x), then du = g'(x) dx. However, can this be explained using function notation? What is function notation’s version of ‘if du/dx = g'(x), then du = g'(x) dx’?

In: Mathematics

Anonymous 0 Comments

Not sure I understand what you mean by function notation but here I go anyway:

When you write “du=g’(x)dx” you are writing what we call a differential for the function u(x). What this means is that whenever you change x by a small amount dx, u changes by a small amount du that equals to g’(x)dx.

But this is exactly what a derivative is.