(Q10.) So, you think you can take the derivative?

TL;DR

Implicitly differentiate the equation and solve for dy/dx.

Transcript

okay for number 10 our equation is 2 cosine x times sine y is equal to 14. and the difference between this equation and the other equations that we have encountered so far is that the y is not isolated so we are just going to take the derivative of this equation implicitly and before i do that we have an equation here let me divide by 2 on both sid... Read More

Key Insights

• ❓ The content demonstrates the process of implicit differentiation for trigonometric equations.
• 📏 The product rule and chain rule play a significant role in finding the derivative.
• ☠️ Isolating dy/dx allows for the determination of the rate of change between variables.

Questions & Answers

Q: What is the equation being implicitly differentiated in the content?

The equation being implicitly differentiated is 2cos(x)sin(y) = 14.

Q: How is the product rule used in the differentiation process?

The product rule is used by keeping the first function (cos(x)) and multiplying it by the derivative of the second function (cos(y)*dy/dx). Additionally, the second function (sin(y)) is kept and multiplied by the derivative of the first function (-sin(x)).

Q: What is the purpose of isolating dy/dx in the equation?

Isolating dy/dx allows us to find the derivative of y with respect to x, which represents the rate of change of y with respect to x.

Q: How is dy/dx finally calculated in the content?

dy/dx is calculated by dividing the right-hand side of the equation by the product of cosine(x) and cosine(y), resulting in tangent(x) * tangent(y).

Summary & Key Takeaways

• The provided content discusses how to implicitly differentiate a trigonometric equation.

• The equation given is 2cos(x)sin(y) = 14.

• Using the product rule and chain rule, the derivative of y with respect to x, dy/dx, is found to be equal to tangent(x) * tangent(y).