y = sin x
find the derivative...
surely your text has a table of derivatives of trig functions. This is such a basic question, you could have looked up the answer in less time than typing in the question.
d/dx (sin x) = cos x
Is there more to this than first appears?
To find the derivative of the function y = sin(x), you can use the concept of differentiation. The derivative of a function represents its rate of change with respect to its independent variable, in this case, x.
The derivative of sin(x) can be found using the chain rule of differentiation. Here's how you can approach it:
Step 1: Identify the function and its dependent variable.
- Function: f(x) = sin(x)
- Dependent variable: y
Step 2: Differentiate the function using the chain rule.
- The derivative of sin(u) with respect to u is cos(u), where u is the function inside the sine function.
- In this case, u = x. Therefore, the derivative of sin(x) is cos(x).
So, the derivative of y = sin(x) is dy/dx = cos(x).
Alternatively, you can also use the trigonometric identity to differentiate sin(x):
- sin'(x) = cos(x)
Therefore, the derivative of y = sin(x) is dy/dx = cos(x).