5. Tangent Planes and Chain Rule

Chain Rule In Multivariable Settings — Quiz

Test your understanding of chain rule in multivariable settings with 5 practice questions.

Practice Questions

Question 1

If $z=f(x,y)$, $x=g(t)$, and $y=h(t)$, which formula gives $\frac{dz}{dt}$?

Question 2

Let $z=x^2y$, with $x=t$ and $y=t^2$. What is $\frac{dz}{dt}$ at $t=1$?

Question 3

If $f(x,y)=x+y$, $x=r\cos\theta$, and $y=r\sin\theta$, what is $f$ written in terms of $r$ and $\theta$?

Question 4

Let $z=x^2+y^2$, where $x=u+v$ and $y=u-v$. What is $\frac{\partial z}{\partial u}$?

Question 5

If $w=f(x,y,z)$ and $x=x(s)$, $y=y(s)$, and $z=z(s)$, which formula gives $\frac{dw}{ds}$?