The Product Rule Importance | York University - Edubirdie

University:
York University
Course:
MATH 1013 | Applied Calculus I
Academic year:

2022
Views:

68

Pages:

1
Author:

Nick T.

The Product Rule [\Delta u = f(x+\Delta x)-f(x)] [\Delta v = g(x+\Delta x)-g(x)] [<0>frac{d}{dx}[f(x)g(x)] = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)g(x+\Delta x)-f(x)g(x)}{\Delta x}] [\frac{d}{dx}[f(x)g(x)] = \lim_{\Delta x \to 0} \frac{f(x+\Delta x)g(x+\Delta x)-f(x)g(x+\Delta x)+f(x)g(x+\Delta x)-f(x)g(x)}{\Delta x}] [\frac{d}{dx}[f(x)g(x)] = \lim_{\Delta x \to 0} \frac{g(x+\Delta x)[f(x+\Delta x)-f(x)]+f(x)[g(x+\Delta x)-g(x)]}{\Delta x}] [\frac{d}{dx}[f(x)g(x)] = \lim_{\Delta x \to 0} g(x+\Delta x) \frac{f(x+\Delta x)-f(x)}{\Delta x} + f(x) \frac{g(x+\Delta x)-g(x)}{\Delta x}] [\frac{d}{dx}[f(x)g(x)] = g(x)f'(x) + f(x)g'(x)]

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