Master the Chain Rule with These Easy Steps - Check Your Work for Accuracy!

[Whatupdoc]

chain rule agian - check my work please

w = -xy-5yz+3xz, x = st, y = exp(st), z = t^2

dw/ds(5,-2) = ________________________

here's what i did:

dw/ds = dw/dx*dx/ds + dw/dy*dy/ds + dw/dz*dz/ds
dw/ds = (3z-y)*(t) + (-x-5z)(exp(st)*t) + (3x-5y)(0)

plug in x,y and z...

dw/ds = (3(t^2)-(exp(st)))*(t) + (-(st)-5(t^2))(exp(st)*t) + (3(st)-5(exp(st)))(0)

now plug in s=5 and t=-2...

dw/ds = (3(5^2)-(exp(5*-2)))*(5) + (-(5*-2)-5(5^2))(exp(5*-2)*-2) + (3(5*-2)-5(exp(5*-2)))(0) = 375.01 which is incorrect. i checked my work three times and i can't find the problem, which means I am doing something wrong

 

[CarlB]

I got -8+39e^{-10} = -7.9982294..., which differs from your result. Is that correct?

I substituted s and t into x, y, and z, so that I didn't have to do the extra step of writing everything out in terms of s and t.

Carl