Partial Derivative

**saccharine** · December 16th 2010, 10:36 AM

Give f(x,y) = sin (x-5t) find partial f/partial S and partial f/partial r

x = (s-6r)^2
t = e^(s^2+r)

**snowtea** · December 16th 2010, 10:41 AM

Use the chain rule.

$\frac{\partial f}{\partial s} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial s} + \frac{\partial f}{\partial t}\frac{\partial t}{\partial s}$

and

$\frac{\partial f}{\partial r} = \frac{\partial f}{\partial x}\frac{\partial x}{\partial r} + \frac{\partial f}{\partial t}\frac{\partial t}{\partial r}$

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