Implicit Differentiation and Related Rates

Question

two variables quantities A and B are found to be related by the equation given below.What is the rate of change dA/dt at the moment when A=3 and dB/dt=2? A^5+B^5=275

Answer 1

Use the chain rule!!

5A⁴ (dA/dt) + 5B⁴ (dB/dt) = 0

Notice that you do not have a value for B which you need.

Use the initial equation to determine B from the given value of A.

Then substitute into the derivative equation and solve for dA/dt.