Find the rate of change of x with respect to p. $$p = \frac { 2 } { 0.00001 x ^ { 3 } + 0.1 x } x \geq 0$$
A) $- \frac { 2 } { p ^ { 2 } \left( 0.00003 x ^ { 2 } + 0.1 \right) }$
B) $- \frac { 2 } { p \left( 0.00003 x ^ { 2 } + 0.1 \right) }$
C) $- \frac { 2 } { p ^ { 2 } x \left( 0.00003 x ^ { 2 } + 0.1 \right) }$
D) $- \frac { 2 } { p x \left( 0.00003 x ^ { 2 } + 0.1 \right) }$
E) $- \frac { 2 x } { p ^ { 2 } \left( 0.00003 x ^ { 2 } + 0.1 \right) }$

Question

Quizplus · Accepted Answer

To find the rate of change of $x$ with respect to $p$, we differentiate both sides of the given equation with respect to $p$, treating $x$ as a function of $p$. The differentiation process involves applying the chain rule and the product rule, leading to the correct answer.

Find the Rate of Change of X with Respect to P