(Above) This is f(x), not f'(x).Bashyboy said:Homework Statement
Find the derivative of f(x) = 1/4 sin^2 2x
The Attempt at a Solution
f'(x) =1/4(sin 2x)^2
Bashyboy said:f'(x) = 1/4*2(sin 2x)(cos 2x)
f'(x) = 1/4(sin 4x)
That is my answer to the problem, but the book has it as f'(x) = 1/2(sin 4x)
What did I do wrong?
The derivative of a trigonometric function is the rate of change of that function at a specific point. It measures how much the output of the function changes when the input is changed by a small amount.
To find the derivative of a trigonometric function, you can use the basic rules of differentiation, such as the power rule, product rule, and chain rule. You can also use the identities and formulas specific to trigonometric functions, such as the derivative of sine, cosine, tangent, and cotangent functions.
The derivative of a trigonometric function is important because it helps us understand the behavior and properties of trigonometric functions. It also has many real-world applications, such as in physics, engineering, and economics, where rates of change are important to analyze and predict.
Sure, let's find the derivative of the sine function, f(x) = sin(x). Using the derivative formula for sine, we get f'(x) = cos(x). This means that at any point on the graph of f(x), the slope of the tangent line is equal to the cosine of that point.
Yes, there are some special cases when finding the derivative of a trigonometric function. For example, the derivative of the tangent function, f(x) = tan(x), is not defined at certain points, namely where cos(x) = 0. This is because the slope of the tangent line at those points would be infinite. Additionally, the derivative of the inverse trigonometric functions have specific rules and formulas that must be used.