How do you use chain rule to find partial derivatives?

1 Answer
Apr 1, 2015

One type of example is as follows: If z=f(x,y), x=g(t), and y=h(t), then you can write dzdt=zxdxdt+zydydt.

For example, if z=x2+y3, x=t4, and y=t5, then zt=2x4t3+3y25t4=8t4t3+15t10t4=8t7+15t14.

You can check that this works by noting that z=x2+y3=t8+t15 so that 8t7+15t14 (so the Chain Rule is more work for this example).

There are other examples where the Chain Rule can be less work.