Answer
y'=$\frac{2}{\sqrt 4t+9}$
Work Step by Step
The chain rule states that if y=g(h(t)), then y'=g'(h(t))h'(t). Since
y=$(4t+9)^{1/2}$, we can set g(t)=$x^{1/2}$ (outside function) and h(t)=4t+9 (inside function), and use the chain rule to find y'. Therefore,
y'=g'(4t+9)h'(t)
We know that
$\frac{d}{dt}$[$t^{1/2}$]=$\frac{1}{2}$$t^{-1/2}$, using the power rule
$\frac{d}{dt}$[4t+9]=4, using the power rule
Now that we know that g'(t)=$\frac{1}{2}$$t^{-1/2}$ and h'(x)=4, we can find y'.
y'=$\frac{1}{2}$$(4t+9)^{-1/2}$(4)
=(4)($\frac{1}{2}$)$(4t+9)^{-1/2}$
=$\frac{2}{\sqrt 4t+9}$
