The derivative of a function is the rate of change of that function at a specific point. In other words, it represents the slope of the tangent line at that point.
To find the derivative of a trigonometric function, you can use the chain rule or the product rule, depending on the form of the function. For example, the derivative of sin(x) can be found using the chain rule as cos(x), while the derivative of cos(x)sin(x) would require the product rule.
The derivative of sine is cosine, and the derivative of cosine is negative sine. This can be remembered using the mnemonic "COsine is NEgative sine."
Yes, the chain rule can be applied to all trigonometric functions, as well as any other type of function. It is a general rule for finding derivatives of composite functions.
Finding the derivative of a trigonometric function is important because it allows us to understand how the function is changing at a given point. This is useful in many applications, such as physics, engineering, and economics, where rates of change play a crucial role.