Use the chain rule to find the derivative

[Mathysics]

Homework Statement

f(x) = ((x^2+2)^2)/(x+2)^1/2
Use the chain rule to find the derivative

Homework Equations

None

The Attempt at a Solution

((x^2+2)^2)(x+2)^-1/2

PS: Answer in the book is 3x((x^2+2)^1/2)

I have no idea how they get it there, would like some help, thx!

 

[Mark44]

Homework Statement

f(x) = ((x^2+2)^2)/(x+2)^1/2
Use the chain rule to find the derivative

Homework Equations

None

The Attempt at a Solution

((x^2+2)^2)(x+2)^-1/2

PS: Answer in the book is 3x((x^2+2)^1/2)

I have no idea how they get it there, would like some help, thx!

It looks like you completely missed the fact that this is a quotient (use the quotient rule first). As part of using the quotient rule, you'll need the chain rule.

 

[Mathysics]

It looks like you completely missed the fact that this is a quotient (use the quotient rule first). As part of using the quotient rule, you'll need the chain rule.

ohh thx! I will try it again (reserved)

 

[Mark44]

BTW, questions on derivatives really should go in the Calculus & Beyond section, not the Precalc section.

 

[HallsofIvy]

Or, since the product rule is (to me anyway) less complicated than the quotient rule, write your function as $f(x) = (x^2+2)^2(x+2)^{-1/2}$ and use the product rule, together with the chain rule.