Calculus Question

Question

If  y=x^3+4x   and  dx/dt=7.   Find  dy/dt when   x=5.

Answer 1

dy/dt = (dy/dx)(dx/dt) = (dy/dx)(7) since we are given that dx/dt = 7

Given that y = x³ + 4x, we know that dy/dx = 3x² + 4

So dy/dt = (dy/dx)(dx/dt) = ( 3x² + 4)(7) = 21x² + 28

At x = 5 dy/dt = 21(5)² + 28 = 525 + 28 = 553

Answer

553