Question

give an example of an implicitly defined curve that was on your homework. find $\frac{dy}{dx}$ for your example. (dont panic if you cant remember the exact details, but do your best.) type your function in the box and show the work of finding the derivative in the show your work section at the end of the recording

Explanation:

Step1: Choose an implicit - function example

Let's take the equation $x^{2}+y^{2}=25$.

Step2: Differentiate both sides with respect to $x$

Differentiating $x^{2}$ gives $2x$, and for $y^{2}$ using the chain - rule, we get $2y\frac{dy}{dx}$. The derivative of the constant 25 is 0. So, $2x + 2y\frac{dy}{dx}=0$.

Step3: Solve for $\frac{dy}{dx}$

First, isolate the term with $\frac{dy}{dx}$: $2y\frac{dy}{dx}=-2x$. Then divide both sides by $2y$ (assuming $y
eq0$) to get $\frac{dy}{dx}=-\frac{x}{y}$.

Answer:

For the implicitly - defined curve $x^{2}+y^{2}=25$, $\frac{dy}{dx}=-\frac{x}{y}$