Well, you're correct. What are the options given?Lion214 said:Homework Statement
Find the derivative of f when
f(x) = cos(sin(x))
The Attempt at a Solution
I used chain rule on this function, and came up with this;
-sin(sin(x)) times cos(x)
Now either I'm doing something completely wrong, or I'm not seeing what it is equivalent to in the answers choices online. I would appreciate some hints on how to go about this.
Mentallic said:Well, you're correct. What are the options given?
Lion214 said:1. f'(x) = -sin(x) cos(sin(x))
2. f'(x) = -cos(x) sin(sin(x))
3. f'(x) = sin(x) cos(cos (x))
4. f'(x) = -cos(x) sin(cos(x))
5. f'(x) = cos(x) sin(sin(x))
6. f'(x) = sin(x) cos(sin(x))
My feeling is that it's the first one, as it is the only one that has a negative sin, but I could be wrong and I'm not sure how could any of these be the same as my original answer.
Ray Vickson said:Why would you say that? You already gave 2) as your answer!
The derivative of a function f at a specific point is the instantaneous rate of change of the function at that point. In other words, it is the slope of the tangent line to the graph of the function at that point.
To find the derivative of a function, you can use the derivative rules such as the power rule, product rule, quotient rule, and chain rule. These rules provide a systematic way to calculate the derivative of a function.
Finding the derivative of a function is important because it helps us understand how the function changes at different points. It is also used in many real-world applications such as physics, economics, and engineering to solve problems involving rates of change.
No, not all functions have a derivative. A function must be continuous and have a defined slope at every point for its derivative to exist. Some functions, such as those with sharp corners or vertical asymptotes, do not have a derivative.
The derivative of a function measures its rate of change, while the antiderivative is the inverse operation of differentiation and can help us find the original function from its derivative. In other words, the derivative tells us how a function changes, while the antiderivative tells us what the original function is.