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The product rule for deriviatives is d/dx f(x)g(x) = g(x) d/dx f(x) + f(x) d/dx g(x).

Think about it. You treat this as two partial deriviatives, one with f(x) and the other with g(x). In each case, the alternate is treated as constant, and can be pulled out of the deriviative. Yes, I know, partial deriviatives is part of multi-variate calculus, which is second year, but I'll leave the first year proof to the reader.

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Q: What is the product rule for derivatives?
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In calculus, to find the derivative of a function, you follow these rules: Power Rule (کتاو قاعدہ), Product Rule (ضرب قواعد), Quotient Rule (تقسیم قاعدہ), Chain Rule (زنجیری قاعدہ), and Trigonometric Rules (ترکیبی قواعد). These rules help determine how the rate of change of a function varies with respect to the input variable.


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