Posted by Lo on October 09, 2002 at 18:57:23:
In Reply to: Re: U Substitution posted by grumpy on October 09, 2002 at 13:53:16:
For derivatives:
Take some term in the equation that is tough to evaluate and replace with U. Then find the derivative of the equation with your substituted U ( derivative of y with respect to U). Then multiply the deivative with the derivative of the original term you replaced. ( u=?????)
Thus you get DY/DU * DU/DX = DY/DX
ex: y=SQRT(x^2+5) u=x^2+5
y=u^.5
Y'=.5U^-.5 * du
Y' = .5 U ^-.5 * (2x dx)
replace x^2+5 for U
y'=.5(X^2+5)^-.5 * 2x dx