Assume x and y are both differentiable functions of t and 3x^9y=30

Question

1. find dy/dt if dx/dt=6 and x=1

2. Find dx/dy if dy/dt=9 and y=2

Answer 1

Step 1:

The differential function is .

Rewrite the differential function is .

Apply derivative on each side with respect to .

Use power rule : .

or

(1)

Step 2:

Find the value of when and .

Substitute and in .

Solution :

Answer 2

(2)

Step 1:

Here consider not .

Find the value of when and .

Substitute and in

Find .

Substitute and in the .

Solution :