Partial derivative problem

Nov 2009
94
6
I have repeated this one several times, and keep getting the same answer. But it's marked wrong, can't find my error:

\(\displaystyle w = xe^{\frac{y}{z}} \)

\(\displaystyle x = t^4 \)
\(\displaystyle y = 6 - t \)
\(\displaystyle z = 1 + 5t \)

\(\displaystyle \frac{dw}{dt} = e^{\frac{y}{z}}(4t^3) + xe^{\frac{y}{z}}(\frac{1}{z})(-1) + xe^{\frac{y}{z}}(\frac{-y}{z^2})(5) \)

\(\displaystyle \frac{dw}{dt} = e^{\frac{y}{z}}(4t^3-\frac{x}{z}-\frac{5xy}{z^2}) \)

(Headbang)

If anyone can explain what I have done wrong, I'd be extremely thankful
 
May 2010
274
67
Los Angeles, California
Your answer looks correct. What makes you think it's not? Remember, books contain misprints and professors can be wrong!