Help with double primes?

I am not sure I know how to do this. If f(x) = x^2/7+4x what is f "(x). I have what f '(x) is which is (4x^2+14x) / (7+4x)^2 but now it is asking for the derivative of that. Can anyone help???

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  • Anonymous
    9 years ago
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    Just use the derivative quotient rule, like you did to start with, and the chain rule. You should end up with something like: (7+4x)^2(8x+14)--(4x^2+14x)[(2(7+4x)(4)] all over [(7+4x)^2]^2.

    I'm not sure if you know what the chain rule is, but I'll try and explain it anyway. On (7+4x)^2, it would be a pain to multiply it out and then find the derivative, so you just treat the numbers in parentheses like a variable. For example, if you had x^2, the derivative would be 2x; so, the first part of the derivative of (7+4x)^2 would be 2(7+4x). For the second part, you just take the derivative of what's inside the parentheses, which would be 4. Multiply those two terms together, and you have your derivative without the hassle of FOILing :)

    Source(s): myself
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