Question

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

Equation                                     Find                                       Given

y = √x                                     (a) dy/dt when x = 4                   dx/dt = 3

                                               (b) dx/dt when x = 25                 dy/dt = 2

Answer 1

Step 1:

The differential function is .

Apply derivative on each side with respect to .

Use power rule : .

or

Step 2:

(a)

Find the value of when .

Substitute in .

.

Step 3:

(b)

Find the value of when .

Substitute in .

.

Solution :

(a) .

(b) .