- #1
ttpp1124
- 110
- 4
- Homework Statement
- Has this been simplified fully?
- Relevant Equations
- n/a
Do you have a question here?ttpp1124 said:Homework Statement:: Has this been simplified fully?
Relevant Equations:: n/a
View attachment 262618
Differentiating a function allows us to find the rate of change of that function at a specific point. Simplifying a function makes it easier to understand and work with, and can reveal important properties of the function.
To differentiate a function, we use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules allow us to find the derivative of a function at a specific point.
The derivative of sin^2(2x) is 4sin(2x)cos(2x). This can be found using the chain rule, where we first take the derivative of the outer function, sin^2(2x), and then multiply it by the derivative of the inner function, 2x.
To simplify this function, we can use the trigonometric identity sin^2(x) + cos^2(x) = 1. This allows us to rewrite the function as f(x) = sin^2(2x) + sin^2(2x) - 1. Then, using the power rule, we can simplify further to f(x) = 2sin^2(2x) - 1.
The final simplified form of f(x) is f(x) = 2sin^2(2x) - 1. This form is easier to work with and can reveal important properties of the function, such as the maximum and minimum values.