What are you doing in the next line? Does it have anything to do with calculus? I don't see any indication that it does.Loppyfoot said:Homework Statement
If f(x) = sin²(3-x), then f ' (0) = ____ .
A. -2cos3
B. -2sin3cos3
C. 6cos3
D. 2sin3cos3
E. 6sin3cos3
Homework Equations
Derivative of Sinx= cosx.
The Attempt at a Solution
I cannot seem to figure out what the derivative would be with this function.
Do you know about the chain rule? That's what you need here. Your function could be written this way f(x) = [sin(3 - x)]2.Loppyfoot said:sin(3-x) * sin(3-x) = Cos(3-x) * Cos(3-x), then plug in 0 for x?
Is there a simpler way using "u" substitution?
Thanks!
Yes, that is correct. That is using the "chain rule".Loppyfoot said:so, would [ sin(3-x)²] = 2[sin(3-x)] * cos(3-x) *-1?
I think what is confusing me is the square of the function.
The derivative of a sine function is the cosine function. This means that if the original function is f(x) = sin(x), then its derivative is f'(x) = cos(x).
To find the derivative of a sine function, you can use the basic rules of differentiation. First, you need to rewrite the sine function in the form of f(x) = sin(x). Then, use the formula f'(x) = cos(x) to find the derivative.
Finding the derivative of a sine function is important because it allows us to understand the rate of change of the function at any given point. This is useful in many real-world applications, such as physics and engineering.
The derivative of a sine function is related to its graph in that the derivative gives us the slope of the function at any given point. This means that the derivative tells us how steep or flat the graph is at a specific point.
The derivative of a sine function can be used to solve problems involving rates of change, optimization, and related rates. By understanding the rate of change of the function, we can determine the maximum or minimum values, as well as how the function is changing over time.