Consider the equation x^2 y - y^3 = z. Assuming x, y, and z depend on time t, find {dy} / {dt}...
Question:
Consider the equation {eq}\displaystyle x^2 y - y^3 = z {/eq}.
Assuming {eq}x,\ y {/eq}, and {eq}z {/eq} depend on time {eq}t {/eq}, find {eq}\dfrac {dy} {dt} {/eq} when {eq}\displaystyle x = 1,\ y = 3,\ \dfrac {dx} {dt} = -2 {/eq}, and {eq}\dfrac {dz} {dt} = 4 {/eq}.
Product Rule of Differentiation:
The derivative of the product of two functions is equal to the sum of "the product of second function and derivative of first function" and "product of first function and derivative of second function".
Answer and Explanation: 1
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Given:
- The given function is {eq}{x^2}y - {y^3} = z, x = 1, y = 3,\dfrac{{dx}}{{dt}} = - 2 {/eq} and {eq}\dfrac{{dz}}{{dt}} = 4 {/eq}.
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Product Rule in Calculus | Overview, Equations & Examples
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Chapter 10 / Lesson 14
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Understand what the product rule is. Learn about the product rule in calculus. Know about the derivative multiplication rule and the product rule equation.
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