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Hello,

I'm having a hard time figuring out which rules to use on this function to take the derivative. (i.e. quotient rule, product rule, etc.) I was wondering if you could help me dissect the function to interpret how to take the derivative.

f(x) = 3 - [(8 + 3x)]^2/3

Thanks you very much.

Nick

Hello,

I'm having a hard time figuring out which rules to use on this function to take the derivative. (i.e. quotient rule, product rule, etc.) I was wondering if you could help me dissect the function to interpret how to take the derivative.

f(x) = 3 - [(8 + 3x)]^2/3

Thanks you very much.

Nick

----------------------------------

An algebraic expression is an indicated sequence of operations. The 'type' of expression is determined by the LAST operation.

If the last operation is multiplication, it's a PRODUCT.

If the last operation is division, it's a QUOTIENT.

If the last operation is addition/subtraction, it's a SUM.

If the last operation is raising to a power(*), it's a POWER.

(*) raising to a power is called involution, but that term was obsolete by the beginning of the LAST century.

.................................

f(x) = 3 - [(8 + 3x)]^2/3 is a SUM, because if I give you x = 47.928, or some such value, you:

Multiply by 3.

Add 8

Raise to the 2/3 power.

Subtract that from 3.

So you 'diff' each term separately -- the sum rule.

...............

Now the second term, I will call: f1(x) = [(8 + 3x)]^2/3 is a POWER, because you

Multiply x by 3.

Add 8

Raise to the 2/3 power.

So you use the power rule, a special case of the chain rule:

Let u = 8 + 3x

f1(x) = u^2/3, where u = 8 + 3x.

I think you can handle it from here.

NOTE: You have redundant bracketing - [(8+3x)]. Typo? Did you mistype the expression?

Calculus

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