Learn How to Find dy/dx using Implicit Differentiation given tan(x) = tanh^2(y)

TL;DR

Implicit differentiation used to find dy/dx in a derivative problem solution.

Transcript

hi everyone in this problem we're being asked to find d y d x which is the derivative so we'll start this problem uh by just taking the derivative of both sides because we have a y here inside this hyperbolic tangent squared we're going to use called implicit differentiation so we'll take the derivative of the left hand side so d dx of the tangent ... Read More

Key Insights

• ❓ Implicit differentiation is a powerful technique in finding derivatives of functions.
• 🖐️ Chain rule plays a crucial role in calculating derivatives involving composite functions.
• 😑 Simplification steps are essential to obtain a clean and concise expression for the derivative.

Questions & Answers

Q: What is the approach used to find dy/dx in this derivative problem?

Implicit differentiation is used in this problem to find dy/dx, where the derivative of both sides is taken and chain rule is applied to the hyperbolic tangent squared function.

Q: How is the derivative of tangent x calculated in this problem?

The derivative of tangent x is secant squared x, which is obtained by differentiating the tangent function with respect to x.

Q: What is the derivative of the hyperbolic tangent squared y in this problem?

The derivative of hyperbolic tangent squared y involves bringing down the exponent, applying chain rule, and simplifying to obtain the final result of dy/dx.

Q: How is the final expression for dy/dx simplified in this problem?

The final expression for dy/dx is simplified by dividing both sides by the necessary terms, resulting in a concise form for the derivative.

Summary & Key Takeaways

• Implicit differentiation used to find dy/dx in a derivative problem.

• Derivative of tangent x is secant squared x.

• Derivative of hyperbolic tangent squared y involves chain rule and simplification steps.