Suppose that x = x(t) and y=y(t) are both functions of t.

Question

 If y = 4 x^2 - 1, and dx/dt = 3 when x = 11, what is dy/dt?

Answer 1

Given data :

y = 4 x² - 1

dx/dt = 3

x = 11

dy/dt = ?

y = 4 x² - 1

Apply derivative with respect to t both sides.

dy/dt = 4(2x)dx/dt

dy/dt = 8x*(dx/dt)

Substitute :

x = 11and dx/dt = 3

dy/dt = 8*11*3

dy/dt = 264