# chain rules

• October 15th 2008, 03:29 PM
iwonder
chain rules
z=x^2y+xy^2
x=5+t^5
y=-2+t^2
how to find dz/dt?
• October 15th 2008, 03:43 PM
skeeter
$\frac{dz}{dt} = x^2\frac{dy}{dt} + 2xy\frac{dx}{dt} + 2xy\frac{dy}{dt} + y^2\frac{dx}{dt} = x^2\frac{dy}{dt} + 2xy\left(\frac{dx}{dt} + \frac{dy}{dt}\right) + y^2\frac{dx}{dt}$

$x = 5+t^5$

$\frac{dx}{dt} = 5t^4$

$y = t^2 - 2$

$\frac{dy}{dt} = 2t$

if you want $\frac{dz}{dt}$ in terms of $t$, perform the substitutions.
• October 15th 2008, 04:01 PM
iwonder