Show that applying the chain rule to z = x / y , where x and y are arbitrary functions of t...
Question:
Show that applying the chain rule to {eq}z= \frac{x}{y} {/eq}, where {eq}x {/eq} and {eq}y {/eq} are arbitrary functions of {eq}t {/eq}, given the quotient rule for functions of one variable.
Quotient Rule:
The quotient rule is one of the general rules that allow you to calculate the derivative of complex expressions.
That is, from the following general formula:
{eq}z\left( t \right) = \frac{{x\left( t \right)}}{{y\left( t \right)}},\quad z'\left( t \right) = \frac{{x'\left( t \right)y\left( t \right) - x\left( t \right)y'\left( t \right)}}{{{y^2}\left( t \right)}} {/eq}.
Answer and Explanation:
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View this answerWritten the function as a function of the variable {eq}t {/eq}, {eq}z = \frac{x}{y} \to z\left( t \right) = \frac{{x\left( t \right)}}{{y\left( t...
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