Problem with understanding Parametric Equation

Question

I was doing the following question:

For the following curves defined parametrically find $\frac{dy}{dx}$ in terms of t and the gradient of the curve for the given value of t:

$x=t^2+4,y=\sqrt(t), t=1$

$\frac{dy}{dt}=\frac{1}{2t^\frac{1}{2}}$

$\frac{dx}{dt}=2t$

using chain rule I found $\frac{dy}{dx}=\frac{\frac{1}{2t^\frac{1}{2}}}{2t}$

but the answer is supposed to be $\frac{1}{4}t^\frac{-3}{2}$

Answer 1

Two things: $\frac{dy}{dt}$ is wrong, though the error is small and easily fixable. Second, you still have some algebraic simplification you haven't done yet. Hint: $\frac{x^a}{x^b} = x^{a - b}$.