Find {eq}\displaystyle\dfrac {\partial z} {\partial x} {/eq} given the following.

{eq}\displaystyle z = 3 x y z - x^6 y^5 + e^{\displaystyle -16 x y^2} {/eq}

## Question:

Find {eq}\displaystyle\dfrac {\partial z} {\partial x} {/eq} given the following.

{eq}\displaystyle z = 3 x y z - x^6 y^5 + e^{\displaystyle -16 x y^2} {/eq}

## Quotient Rule:

If the expression given is in the form of a fraction them the derivation of that expression can be done with the help of the division rule. Suppose the expression is {eq}\dfrac{u}{v} {/eq}, then the partial derivation will be of the form {eq}\dfrac{\partial }{{\partial x}}\left( {\dfrac{u}{v}} \right) = \dfrac{{u'v - uv'}}{{{v^2}}} {/eq}.

## Answer and Explanation: 1

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**Given:**

- The expression {eq}z = 3xyz - {x^6}{y^5} + {e^{ - 16x{y^2}}} {/eq}.

Rewrite the expression {eq}z = 3xyz - {x^6}{y^5} + {e^{ -...

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Chapter 18 / Lesson 12What 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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