Derivatives in parametric form
Derivatives in parametric form
Last updated at Dec. 16, 2024 by Teachoo
Ex 5.6, 1 If x and y are connected parametrically by the equations without eliminating the parameter, Find ๐๐ฆ/๐๐ฅ, x = 2ใ๐๐กใ^2, y = ใ๐๐กใ^4Here ๐๐ฆ/๐๐ฅ = (๐๐ฆ/๐๐ก)/(๐๐ฅ/๐๐ก) Calculating ๐ ๐/๐ ๐ ๐ฆ = ใ๐๐กใ^4 ๐๐ฆ/๐๐ก " =" ใ4๐๐กใ^(4 โ1) "=" ใ4๐๐กใ^3 Calculating ๐ ๐/๐ ๐ ๐ฅ = 2ใ๐๐กใ^2 ๐๐ฅ/๐๐ก " =" 2 ร 2๐๐ก "=" 4๐๐ก Now, ๐๐ฆ/๐๐ฅ = (๐๐ฆ/๐๐ก)/(๐๐ฅ/๐๐ก) Putting values ๐๐ฆ/๐๐ฅ = (4๐๐ก^3)/4๐๐ก ๐ ๐/๐ ๐ = t2