- #1
micromass said:Yes, the final answer is correct. But if I was your teacher I would have given 2/4 too. The point is that your notation is really messy and you can't really see what you're doing And you're making the problem longer than it needs to be...
gurtaj said:She said you can expand that answer even more
gb7nash said:Ohhhh, I see what's going on here.
Hint: Look and sinh and cosh.
You still the problem right though. I can't see why your teacher would give you half credit.
(Also, look at tanh)
gb7nash said:I have no idea then. I think your instructor's crazy.
A derivative in calculus is a measure of the rate at which a function changes. It represents the slope of a tangent line to a curve at a given point and is calculated using the limit concept. In simpler terms, it shows how much a function is changing at a specific point.
To find the derivative of a function, you need to use the rules of differentiation. These rules include the power rule, product rule, quotient rule, and chain rule. You can also use the limit definition of a derivative to find the derivative of a function.
The derivative is important in calculus because it has many practical applications in fields such as physics, engineering, economics, and more. It is used to solve optimization problems, find maximum and minimum values, and analyze the behavior of a function at a specific point.
The derivative and the rate of change are closely related concepts, but there is a subtle difference between them. The derivative is a general concept that applies to functions, while the rate of change is specific to a particular variable. In other words, the derivative measures the overall rate of change of a function, while the rate of change measures the change of a specific variable within that function.
No, you cannot have a derivative at a point where a function is not defined. The definition of a derivative requires the function to be continuous at the point where you are trying to find the derivative. If the function is not defined at that point, it cannot be continuous and therefore cannot have a derivative.