- #1

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## Homework Statement

if p(x)= f(x^3), find P'(1)

## Homework Equations

## The Attempt at a Solution

can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?

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- Thread starter Willian93
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- #1

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if p(x)= f(x^3), find P'(1)

can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?

- #2

cepheid

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## Homework Statement

if p(x)= f(x^3), find P'(1)

Are both p's supposed to have the same case here (i.e. are they the same symbol representing the same function?) If not, then this question doesn't make much sense.

can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?

No, not quite. If I understand the problem right, then what you have is a composite function, and you need to use the chain rule, and you need to know what the functional form of f(x) is. Is f(x) given?

One way of looking at it: p(x) = f(g(x)) where g(x) = x

Another equivalent way to look at it: f(x

Edit: Those two ways of looking at it are not really different at all, since in the latter case, I just defined a new variable u = g(x) = x

- #3

Char. Limit

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Also, the derivative of x^3 is not 2x^2.

- #4

HallsofIvy

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No. The## Homework Statement

if p(x)= f(x^3), find P'(1)

## Homework Equations

## The Attempt at a Solution

can i do the derivative of x^3 is 2x^2, then substitute to get f(2x^2)?, then substitute 1 for x?

- #5

cepheid

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(And, as Cepheid said, the derivative of x^3 is NOT "2x^2".)

Actually, Char. Limit said that. It was a good catch...

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