What is the difference between the chain rule and the product rule in calculus?
An example of an AI chatbot conversation about the chain rule and product rule in calculus.
What is the difference between the chain rule and the product rule in calculus?
The chain rule is used to differentiate composite functions, while the product rule is for differentiating products of functions.
Can you give me an example of the chain rule?
Sure! If you have a function like f(g(x)), the chain rule states that the derivative is f'(g(x)) * g'(x).
And what about the product rule?
For the product rule, if you have two functions u(x) and v(x), the derivative is u'v + uv'.
Can you show me a specific example using both rules?
Absolutely! For the chain rule, if f(x) = sin(x^2), the derivative is cos(x^2) * 2x. For the product rule, if u(x) = x and v(x) = e^x, the derivative is e^x + xe^x.
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