Derivative of the Product of Two Functions: Applying the Chain Rule

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Homework Statement


take the derivative of a(t) = b(t)c(t)

Homework Equations


chain rule

The Attempt at a Solution


Apply the chain rule: a'(t) = c(t)b'(t) + b(t)c'(t)
Is this correct? Thank you.
 
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harpf said:

Homework Statement


take the derivative of a(t) = b(t)c(t)

Homework Equations


chain rule

The Attempt at a Solution


Apply the chain rule: a'(t) = c(t)b'(t) + b(t)c'(t)
Is this correct? Thank you.

Yes, it's correct. But that's called the product rule, not the chain rule.
 
Thanks. I appreciate your response.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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