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 $f^{\prime }(t)=-2(t-9{)}^{-3/2}\ast 1=-2/(t-9{)}^{3/2}$

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

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 ：$\boxed{{\displaystyle y=-2x/125+168/125}}$ is the equation of the tangent line