Copyright

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

Become a Study.com member to unlock this answer!

View this answer


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^{ -...

See full answer below.


Learn more about this topic:

Loading...
Partial Derivative: Definition, Rules & Examples

from

Chapter 18 / Lesson 12
24K

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


Related to this Question

Explore our homework questions and answers library