Question

Suppose that f(x)=sqrt(4+sqrt(3x)) Find f'(x) Using the Chain rule
Please help I have been trying to figure this out all day.
So far I have this (1/2(4+sqrt3)^-1/2) (1/2(sqrt3)^-1/2)

Answer 1

ok you need to rewrite you function in index notation to make it easier...

\[y= ( 4 +(3x)^{\frac{1}{2}})^{\frac{1}{2}}\]

so now let \[u = 4 + (3x)^{\frac{1}{2}}\]

then

\[y = u^{\frac{1}{2}}\]

find \[\frac{dy}{du}\]

also find

\[\frac{du}{dx} \]

then \[f'(x) = \frac{dy}{du} \times \frac{du}{dx}\]

Answer 2

so you solution looks correct so far

\[\frac{1}{2}( 4 + \sqrt(3x))^{-\frac{1}{2}} \times \frac{1}{2}(3x)^{-\frac{1}{2}}\]

now you need to be able to write it without index notation.

the 1st part is

\[\frac{1}{2} \times \frac{1}{\sqrt{4 + \sqrt{3x}}}\]

Answer 3

So would the next one be 1/2*(1/sqrt3x)?

Answer 4

correct...

Answer 5

so you will have

\[\frac{1}{2\sqrt{4 + \sqrt{3x}}} \times \frac{1}{2\sqrt{3x}}\]

just simplify this

Answer 6

This isn't be accepted as the correct answer.