Use the chain rule to find partial z / partial s and partial z / partial t, where z=x^2+xy+y^2,...


Use the chain rule to find {eq}\displaystyle \frac{\partial z }{ \partial s} {/eq} and {eq}\displaystyle \frac{\partial z }{ \partial t} {/eq}, where {eq}z=x^2+xy+y^2,\ x=3s + 4t,\ y=5s + 6t {/eq}.

The Chain Rule For Multi-Variable Functions:

Just as there is the chain rule for derivation of functions in one variable, it also exists for derivation of multi-variable functions. In the case of several variables, the chain rule is applied by means of an additive formula in which partial derivatives are considered with respect to each of the variables independently.

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{eq}z=x^2+xy+y^2,\ x=3s + 4t,\ y=5s + 6t {/eq}

We need to calculate the derivatives {eq}\displaystyle \frac{\partial z}{\partial...

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Partial Derivative: Definition, Rules & Examples


Chapter 18 / Lesson 12

What is a Partial Derivative? Learn to define first and second order partial derivatives. Learn the rules and formula for partial derivatives. See examples.

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