Suppose $f(t)=\frac{4}{\sqrt{t-9}}$
(a) Find the derivative of $f$.
$f^{\prime}(t)=$
(b) Find an equation for the tangent line to the graph of $y=f(t)$ at the point $(t, y)=(34,4 / 5)$.

Tangent line: $y=$

Step 1 ：Rewrite \(f(t)\) as \(f(t) = 4(t-9)^{-1/2}\)

Step 2 ：Identify the outer function as \(4x^{-1/2}\) and the inner function as \(t-9\)

Step 3 ：Find the derivative of the outer function to get \(-2x^{-3/2}\)

Step 4 ：Find the derivative of the inner function to get \(1\)

Step 5 ：Apply the chain rule to find the derivative of \(f(t)\), which is \(f'(t) = -2(t-9)^{-3/2} * 1 = -2/(t-9)^{3/2}\)

Step 6 ：Substitute \(a = 34\), \(f(a) = 4/5\), and \(f'(a) = -2/(34-9)^{3/2} = -2/125\) into the equation of the tangent line \(y = f'(a)(x - a) + f(a)\)

Step 7 ：Simplify the equation of the tangent line to get \(y = -2/125x + 68/125 + 4/5 = -2/125x + 168/125 = -2x/125 + 168/125\)

Step 8 ：\(\boxed{y = -2x/125 + 168/125}\) is the equation of the tangent line