Implicit Differentiation a^2 + b^2 = c^2, determine da/dt when a = 5, b = 12, and c = 13, if db/dt = 3 and c(t) = t^2 -3t

Question

a^2 + b^2 = c^2, determine da/dt when a = 5, b = 12, and c = 13, if db/dt = 3 and c(t) = t^2 -3t

Please show steps, the answers the text book gives me are 13.106 and -27.506.

Answer 1

Use implicit differentiation for the first equation:

2a da/dt + 2b db/dt = 2c dc/dt

We're given a, b, c, and db/dt. We have to find dc/dt

c(t) = t² - 3t

Also c = 13, so solve for t

Next dc/dt = 2t - 3

Plug in the values of t that you solved for to get two values for dc/dt

Now you have dc/dt. Plug in and solve for da/dt