missed a calc lesson and trying to play catch up. a little confused on this one:
find the derivative of the function using chain rule or logarithmic differentiation
f(x) = (x^2 + 2)^200 * (x^3 - x)^10
any step by step help is greatly appreciated
missed a calc lesson and trying to play catch up. a little confused on this one:
find the derivative of the function using chain rule or logarithmic differentiation
f(x) = (x^2 + 2)^200 * (x^3 - x)^10
any step by step help is greatly appreciated
Hello, JGaraffa!
I'll do it both ways for you . . .
Differentiate using the chain rule or log differentiation:
. .
Product and Chain Rules:
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Factor: .
. . . . . . . . .
. . . . . . . . .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Logarithmic Differentiaton:
Take logs:
. .
. . . . . .
. . . . . .
Differentiate implicitly:
. .
. . . .
. . . .
. . . .
. . . .
. . . .
thanks for your help!
i set mine up a little differently, however
i used (x^2 + 2)^200 as f(x)
and (x^3 - x)^10 as g(x)
so when i did chain rule it came out as
f`(x) = 2x[200(x^2 + 2)^199]
g`(x) = 3x^2[10(x^3 - x)^9]
right so far?
then i used product rule and came up with:
2x[200(x^2 + 2)^199] * (x^3-x)^10 + (x^2)^200 * 3x^2[10(x^3 - x)^9]
right? a little confused how to simplify from here. can you help?
usually my prof lets us leave it like this but i may as well leave that as well as the way you simplified it, just in case.
thanks again!