Two variables a and b are related by the equation a4b3 125

Two variables a and b are related by the equation a⁴b³ = 125. At a = 1, b is increasing at the rate of 2 units per second. Find the rate of a.

a. -10/3

b. -0.3

c. 0.3

d. 10/3

Solution

differentiate

4a^3b^3 da/dt + 3b^2a^3 db/dt = 0

when a=1 , b=5 , and db/dt =2 ,da/dt=?

4(1)^3*5^3 da/dt + 3(5)^2*(1)^3 *2 =0

500 da/dt + 150 = 0

500 da/dt = -150

da/dt = -150/500 = -.3

answer is option b. - 0.3