Question

w = xe^y /z, x = t^6, y = 9 - t, z = 4 + 8t

Answer 1

total differential?

Answer 2

Its the chain rule to find dw/dt

Answer 3

multivariable chain rule is:

\[dw = f_xdx +f_ydy +f_zdz \]
divide by dt to get

\[\large \frac{dw}{dt}=f_x \frac{dx}{dt}+f_y\frac{dy}{dt}+f_z\frac{dz}{dt} \]

Answer 4

I keep getting the wrong answer for my homework

Answer 5

the rest is only substitution, \[ \frac{dx}{dt}= 6t^5 \]
\[ \frac{dy}{dt}=-1\]
\[ \frac{dz}{dt}=8 \]

Answer 6

and the rest are partial derivatives of the function itself.