SOLUTION: Please Help, Use the chain rule of partial differentiation to find df/dt in terms of t where f(x, y) = e^(2x-3y) and x = t^2, y = 1/t. Check the result by direct substitution

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: Please Help, Use the chain rule of partial differentiation to find df/dt in terms of t where f(x, y) = e^(2x-3y) and x = t^2, y = 1/t. Check the result by direct substitution       Log On


   

Question 381641: Please Help,
Use the chain rule of partial differentiation to find df/dt in terms of t where f(x, y) = e^(2x-3y) and x = t^2,
y = 1/t.
Check the result by direct substitution for x and y in f(x, y), followed by ordinary differentiation with respect
to t.
Hence show that when t = 1, df/dt = 7/e.
Thank You
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
df%2Fdt=%28df%2Fdx%29%2A%28dx%2Fdt%29%2B%28df%2Fdy%29%2A%28dy%2Fdt%29

df%2Fdt=4t%2Ae%5E%282t%5E2-3%2Ft%29%2B3%2Ft%5E2e%5E%282t%5E2-3%2Ft%29
df%2Fdt=e%5E%282t%5E2-3%2Ft%29%284t%2B3%2Ft%5E2%29
When t=1
df%2Fdt=e%5E%282-3%29%284%2B3%29
highlight%28df%2Fdt=7%2Fe%29
I get that too.
Well done.