(1 point) Suppose that $x = x (t)$ and $y = y (t)$ are both functions of $t$ . If
$y = 4 x^{2} - 1,$
and $d x / d t = 4$ when $x = 19$ , what is $d y / d t$ ?
$d y / d t =$

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$\frac{d y}{d t} = 608$ when $x = 19$ .

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Step 1 ：Given the function $y = 4 x^{2} - 1$ , we can differentiate it with respect to $x$ to get $\frac{d y}{d x} = 8 x$ .

Step 2 ：We know that $\frac{d y}{d t} = \frac{d y}{d x} \cdot \frac{d x}{d t}$ .

Step 3 ：We are given that $\frac{d x}{d t} = 4$ when $x = 19$ .

Step 4 ：Substitute these values into the equation to find $\frac{d y}{d t}$ : $\frac{d y}{d t} = 8 x \cdot \frac{d x}{d t} = 8 \cdot 19 \cdot 4 = 608$ .

Step 5 ： $\frac{d y}{d t} = 608$ when $x = 19$ .

(1 point) Suppose that x=x(t) and y=y(t) are both functions of t. Ify=4x2−1,and dx/dt=4 when x=19, what is dy/dt ?dy/dt=

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(1 point) Suppose that $x = x (t)$ and $y = y (t)$ are both functions of $t$ . If
$y = 4 x^{2} - 1,$
and $d x / d t = 4$ when $x = 19$ , what is $d y / d t$ ?
$d y / d t =$