- #1
Gondur
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Homework Statement
y=1 / (cos h x), find dy/dx
Homework Equations
chain rule and coshx=(e^x+e^-x)/2
Curious3141 said:Resize your image! Way too big.
The most obvious error is ##\frac{dy}{du} = \ln |u|##. Sure that's the derivative, and not the integral?
Other than that, for Chain Rule, it's generally not helpful to substitute variables like this. Not wrong, but it can overcomplicate things.
SteamKing said:Start with the definition of cosh(x) in terms of the exponentials and re-write 1/cosh(x). What is dy/dx when y = 1/x or x^-1?
Gondur said:What an idiot I am. This mistake is proof that I am tired and should get some sleep. Well what other method do you suggest I use, I'd definitely like to know if it's more efficient.
You can resize my image by clicking Ctrl and - on the keyboard. If you have a mouse with a wheel then turn the wheel towards you (downwards) while holding down Ctrl
Hyperbolic differentiation is a mathematical concept that involves taking the derivative of a hyperbolic function. It is similar to traditional differentiation, but with hyperbolic functions such as sinh, cosh, and tanh instead of trigonometric functions like sine and cosine.
The purpose of hyperbolic differentiation is to calculate the instantaneous rate of change of a hyperbolic function at a specific point. It is commonly used in physics and engineering to model and analyze systems with exponential growth or decay.
Hyperbolic differentiation uses the hyperbolic functions as the base for finding derivatives, while traditional differentiation uses trigonometric functions. Hyperbolic functions have different properties and rules for differentiation compared to trigonometric functions, making the process slightly different.
Hyperbolic differentiation has various applications in physics, engineering, and economics. It can be used to model systems with exponential growth or decay, such as population growth or radioactive decay. It is also used in signal processing, control systems, and other areas of mathematics and science.
Yes, there are limitations to hyperbolic differentiation. It is not applicable to all types of functions, and can only be used for hyperbolic functions. Additionally, it may not always provide an accurate representation of a system, as it assumes a constant rate of change and does not account for external factors or other variables.