- #1
domyy
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Homework Statement
x3 - sin 2x
Find f'(∏/6)
The Attempt at a Solution
f'(x) = 3x2 - 2 cos 2x
f(∏/6) = 2700 - 2 [ (√3/2) ] ---> from 2 [ cos(∏/6)]
answer: 2700 - √3
My book has the answer as (∏2 - 12)/12
domyy said:Oh I was thinking of ∏ = 180.
Is it wrong? =/
The general formula for finding the derivative of a trigonometric function is: d/dx(sin x) = cos x and d/dx(cos x) = -sin x. This can be extended to other trig functions such as tangent, cotangent, secant, and cosecant using the quotient rule.
The process for finding the derivative of a trigonometric function involves applying the chain rule and the derivative formulas for sine and cosine. First, rewrite the function in terms of sine and cosine. Then, apply the chain rule to find the derivative of the function. Finally, use the derivative formulas for sine and cosine to simplify the expression.
The derivative of a trigonometric function changes with respect to the angle based on the trigonometric identity d/dx(sin x) = cos x and d/dx(cos x) = -sin x. This means that the derivative of a trigonometric function is dependent on the value of the angle being evaluated.
Yes, there are special cases when finding the derivative of a trigonometric function. For example, when taking the derivative of tangent or cotangent, the quotient rule must be used. Also, when taking the derivative of secant or cosecant, the product rule must be used.
Understanding the derivative of trigonometric functions is important because it allows us to find the rate of change of these functions, which is useful in many applications, such as physics and engineering. It also helps us to better understand the behavior of these functions and their derivatives can be used to solve more complex problems involving trigonometric functions.