Question

Suppose that x=x(t) and y=y(t) are both functions of t. If y=2x^2-1 and dx/dt=6 when x=11 what is dy/dt?

Answer 1

Step 1: Can you take the derivative of the equation y=2x^2-1

Answer 2

y'=4x

Answer 3

\(\left. \dfrac{dy}{dt} \right|_{x = 11} = \left. \dfrac{dy}{dx} \right|_{x = 11} \cdot \left. \dfrac{dx}{dt}\right|_{x = 11}\)

\(= \left. 4x \right|_{x = 11} \cdot \left. \dfrac{dx}{dt}\right|_{x = 11}\)

\(= 44 \cdot 6\)

Answer 4

Thank you!! that makes sense I was having a hard time interpreting the instructions