Calculus Homework: Derivative of g(x) = x * sqrt(4-x) using Product Rule

[Chaubin]

Homework Statement

Find the derivative of g(x)=x * sqrt(4-x)

Homework Equations

The Attempt at a Solution

I know I use the product rule, but I am not sure how to derive the sqrt(4-x) portion.

 

[tiny-tim]

Welcome to PF!

Hi Chaubin! Welcome to PF!

(have a square-root: √ )

… I am not sure how to derive the sqrt(4-x) portion.

Hint: rewrite it as (4 - x)^1/2

 

[fss]

What's another way to write sqrt(4-x), say... with exponents?

 

[Chaubin]

So, I take the quantity (4-x)^1/2 and turn it into (1/2)*(4-x)^-1/2? Is that it?

 

[fss]

So, I take the quantity (4-x)^1/2 and turn it into (1/2)*(4-x)^-1/2? Is that it?

Remember the chain rule.

 

[tiny-tim]

(try using the X² icon just above the Reply box )

you've left out the coefficient of x

 

[Chaubin]

Ok, i think I finished it.
I ended up with (x/((2 * sqrt(4-x))) + sqrt(4-x)

 

[tiny-tim]

Ok, i think I finished it.
I ended up with (x/((2 * sqrt(4-x))) + sqrt(4-x)

no, that would work for √(x-4), but not for √(4-x)

(and your brackets are in the wrong place)

 

[Chaubin]

I know the derivative of sqrt(4-x) is -1/(2*sqrt(4-x)).
After this I get a bit foggy on the procedure.
I think I have to use the product rule f(x)*g(x)= f(x)*g'(x) + f'(x)*g(x)
In this case f(x) = x and g(x)= sqrt(4-x).
So it should be:
x*(-1/(2*sqrt(4-x)) + 1 * sqrt(4-x)

correct?

 

[tiny-tim]

Hi Chaubin!

(just got up :zzz: …)

x*(-1/(2*sqrt(4-x)) + 1 * sqrt(4-x)

correct?

Yup!