How to Find the Derivative of Inverse Hyperbolic Sine

TL;DR

To find the derivative of the inverse hyperbolic sine, use either the natural logarithm method, yielding 1/(√(1+x²)), or apply implicit differentiation, which leads to the same result. Both methods confirm that the derivative is 1/(√(1+x²)).

Transcript

okaying stevia i will show you guys two ways to find the derivative of the inverse hyperbolic sine X for the first way is that we need to know the inverse hyperbolic sine X it's actually the same as Ln of X plus square root of x squared plus 1 I did do a video on that so if you have a signal video pc iguess watch that so i can just go ahead and dif... Read More

Key Insights

• 👨‍💼 The derivative of the inverse hyperbolic sine X can be found using two different methods: by applying the derivative rule for the natural logarithm or by using implicit differentiation.
• 🫚 The first method involves differentiating the natural logarithm of X plus the square root of x^2 + 1 and applying the chain rule.
• ❓ The second method involves using implicit differentiation and rearranging the equation to solve for the derivative.
• ❓ The results obtained from both methods are the same, giving the derivative as 1/(√(1+x^2)).

Questions & Answers

Q: What is the first method demonstrated in the video for finding the derivative of the inverse hyperbolic sine X?

The first method involves using the natural logarithm of X plus the square root of x^2 + 1, and applying the derivative rule for the natural logarithm.

Q: How is the chain rule used in the first method?

The chain rule is applied by multiplying the derivative of the inside function (x^2 + 1) with the derivative of the square root function (√(x^2 + 1)).

Q: What is the result obtained from the first method?

The result obtained from the first method is 1/(√(x^2 + 1)).

Q: What is the second method demonstrated in the video for finding the derivative of the inverse hyperbolic sine X?

The second method involves using implicit differentiation and rearranging the equation to solve for dy/dx.

Q: What is the derivative obtained from the second method?

The derivative obtained from the second method is 1/(√(1+x^2)).

Q: Are the results obtained from both methods the same?

Yes, both methods yield the same result of 1/(√(1+x^2)).

Summary & Key Takeaways

• The video shows the first method of finding the derivative of the inverse hyperbolic sine X using the natural logarithm.

• The second method of finding the derivative is demonstrated using implicit differentiation.

• Both methods yield the same result of 1/(√(1+x^2)), which is the derivative of the inverse hyperbolic sine X.