Find d/dx of hyperbolic function

In summary, the conversation discusses finding the derivative of a hyperbolic function and the use of Maple to check the answer. The solution is provided and it is suggested to use trig identities to show the equality. The use of specific values of x can also help confirm the correctness of the answer.
  • #1
[SOLVED] find d/dx of hyperbolic function

Homework Statement


Find:
http://www.mcp-server.com/~lush/shillmud/1.1A.Q.JPG

Homework Equations


d/dx f(x)*g(x) = f(x) * d/dx g(x) + g(x) * d/dx f(x)
d/dx f(g(x)) = d/dx f(g(x))* d/dx g(x)
d/dx sinh x = cosh x
d/dx cosh x = sinh x

The Attempt at a Solution


http://www.mcp-server.com/~lush/shillmud/1.1A.A.JPG

Can this be further simplified? When I run it in maple I get:
http://www.mcp-server.com/~lush/shillmud/1.1A.C.JPG

I'm probably going to be posting here often so let me give you a little background. I am beginning calc II by correspondence. It is the last course of my undergrad and I haven't done any pure math courses in a while. I think things are going alright so far but without a prof or fellow students I sometimes become stuck or find it difficult to check an answer in a way that allows me to move on to the next question with confidence. I thought maple might help me check my answers but in this case it's left me more confused. Thanks for reading!

P.S. How do I use special math characters (like infinite etc.) in my post as have seen some people do?
 
Last edited:
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  • #2
What you have is perfectly correct. I can't speak for the Maple (especially not if they include "ln(e)" in the answer!
 
  • #3
I expect it's simply a matter of applying a (hyperbolic) trig identity to show they are equal.

Plugging in 5 or 6 (non-special!) values of x should, at least, give you high confidence that those expressions are, in fact, equal.
 

What is the definition of a hyperbolic function?

A hyperbolic function is a type of mathematical function that is defined by the relationship between the exponential function and the trigonometric functions. It is commonly used in calculus to model real-world phenomena, such as the shape of a hanging chain or the trajectory of a rocket.

What is the general form of a hyperbolic function?

The general form of a hyperbolic function is f(x) = a * sinh(bx) or f(x) = a * cosh(bx), where a and b are constants.

How do you find the derivative of a hyperbolic function?

To find the derivative of a hyperbolic function, you can use the chain rule. For example, to find the derivative of sinh(x), you would use the formula d/dx sinh(x) = cosh(x).

What is the relationship between hyperbolic functions and trigonometric functions?

Hyperbolic functions are closely related to trigonometric functions. In fact, the names of the hyperbolic functions, such as sinh and cosh, are derived from the names of their trigonometric counterparts, sine and cosine. Additionally, the identities and properties of trigonometric functions can also be applied to hyperbolic functions.

How are hyperbolic functions used in real-world applications?

Hyperbolic functions are used in a variety of real-world applications, including physics, engineering, and finance. They can be used to model the behavior of systems and processes, such as oscillations, vibrations, and exponential growth. They are also used in calculus to solve problems involving optimization and rates of change.

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