Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt.

Question

y = √x

(a) Find dy/dt, given x = 9 and dx/dt = 5.

dy/dt = 

(b) Find dx/dt, given x = 64 and dy/dt = 4.

dx/dt = 

Answer 1

y = √x

(a) dy/dt = 1/2 x^-1/2 dx/dt

at x=9, dx/dt =5

dy/dt =( 1/2) (9) ^-1/2 (5)

= 5/6

(b) y = √x

dy/dt = (1/2) x^-1/2 dx/dt

dx/dt = 2 x^1/2 dy/dt

at x= 64, dy/dt =4

dx/dt = 2* 8 *4

=64