Sect 3 11 #32, derivative of cosh(ln(x))

TL;DR

Learn two different methods to differentiate cosh(x) and find the final answer using algebraic manipulation.

Transcript

let's talk about how we can differentiate cause of our necks and I'm going to show you guys two ways for this question the first way is I'm just going to look at this expression and take the root of that and we'll begin by saying okay G prime of X and we'll first ask ourselves what's the derivative of cosh and the answer is positive 6 so we have a ... Read More

Key Insights

• 😑 There are two methods for differentiating cosh(x): one involves directly taking the derivative and the other involves substituting x into the expression.
• 😒 The first method uses the chain rule to multiply the derivative of cosh(x) by the derivative of the inner function.
• 😑 The second method simplifies the expression for cosh(x) before taking the derivative.
• 🥺 Both methods lead to the same final answer.
• ❓ In the first method, the derivative of cosh(x) is positive 6.
• 😑 In the second method, the simplified expression for cosh(x) is X + X^(-1).

Questions & Answers

Q: What are the two methods for differentiating cosh(x)?

The first method involves taking the derivative of cosh(x) and applying the chain rule. The second method involves substituting x into the expression for cosh(x) and simplifying before taking the derivative.

Q: How does the first method work?

The first method involves taking the derivative of cosh(x), which is positive 6. Then, using the chain rule, we multiply this by the derivative of the inside function, Ln x, which is 1/x.

Q: What is the second method for differentiating cosh(x)?

The second method involves substituting x into the expression for cosh(x) and simplifying it. Then, we take the derivative of the simplified expression.

Q: How does the second method work?

In the second method, we substitute x into the expression for cosh(x) and simplify it to X + X^(-1). Then, we take the derivative of this simplified expression.

Summary & Key Takeaways

• The content explains two methods to differentiate cosh(x).

• The first method involves taking the derivative of cosh(x) and then applying the chain rule.

• The second method involves substituting x into the expression for cosh(x) and simplifying before taking the derivative.