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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Partial Derivative: Definition, Rules & Examples
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Chapter 18 / Lesson 12
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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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