Chain rule agian - check my work

  • Thread starter Whatupdoc
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  • #1
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chain rule agian - check my work plz

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 cant find the problem, which means im doing something wrong
 

Answers and Replies

  • #2
CarlB
Science Advisor
Homework Helper
1,231
25
I got [itex]-8+39e^{-10} = -7.9982294...[/itex], 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
 

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