To find given , you can use implicit differentiation. The equation is not given in the form , so we will differentiate both sides of the equation with respect to using implicit differentiation.

Start by differentiating both sides of the equation:

.

Now, differentiate each term on the left side of the equation separately:

1. .
2. is a bit more involved because it’s a composite function. You can use the chain rule, which states that . In this case, and . So, applying the chain rule:

.

Now, differentiate the right side of the equation:

.

Now, you can rewrite the equation with these derivatives:

To provide the best experiences, we use technologies like cookies to store and/or access device information. Consenting to these technologies will allow us to process data such as browsing behavior or unique IDs on this site. Not consenting or withdrawing consent, may adversely affect certain features and functions.

Functional
Always active

The technical storage or access is strictly necessary for the legitimate purpose of enabling the use of a specific service explicitly requested by the subscriber or user, or for the sole purpose of carrying out the transmission of a communication over an electronic communications network.

Preferences

The technical storage or access is necessary for the legitimate purpose of storing preferences that are not requested by the subscriber or user.

Statistics

The technical storage or access that is used exclusively for statistical purposes.The technical storage or access that is used exclusively for anonymous statistical purposes. Without a subpoena, voluntary compliance on the part of your Internet Service Provider, or additional records from a third party, information stored or retrieved for this purpose alone cannot usually be used to identify you.

Marketing

The technical storage or access is required to create user profiles to send advertising, or to track the user on a website or across several websites for similar marketing purposes.

This answer was edited.To find given , you can use implicit differentiation. The equation is not given in the form , so we will differentiate both sides of the equation with respect to using implicit differentiation.

Start by differentiating both sides of the equation:

.

Now, differentiate each term on the left side of the equation separately:

1. .

2. is a bit more involved because it’s a composite function. You can use the chain rule, which states that . In this case, and . So, applying the chain rule:

.

Now, differentiate the right side of the equation:

.

Now, you can rewrite the equation with these derivatives:

.

Now, isolate the term with :

.

Factor out :

.

Now, solve for by dividing both sides by :

.

Simplify the expression:

.

So, if .