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toney32 toney32
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11 years ago
for example if you have y=sin(x^5+x) and you want to find the derivative. why do you treat it as a chain rule and not a product rule?
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wrote...
11 years ago
You have a function inside of a function. You aren't multiplying sine by anything, because that wouldn't make sense. Sine is a function of the things inside the parentheses.
wrote...
11 years ago
You don't use the product rule because it's not a product like f(x)g(x).  It's not sin(x) times (x^5+x), it's an example of a composite formula, sine of (x^5 +x), like f(g(x).  So the chain rule applies, f'(g(x)(g'(x))

y' = cos(x^5 +x) times (5x*4 + 1)

because derivative of sin = cos, etc.
wrote...
11 years ago
The derivative of a sine is cosine. But you inside the parenthesis you still have a function which you need to find its derivative!

So:
Cos(x^5+x) . (5x^4+1)
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