Question

Use the rules of differentiation to find the derivative of the function.
y =π/3 cos(θ)

Answer 1

The derivative of the function y = π/3 cos(θ) is y' = -(π/3) sin(θ), following the constant multiple rule and the derivative of cosine in differentiation.

Step-by-step explanation:

To find the derivative of the function y = π/3 cos(θ) using the rules of differentiation, we will apply the constant multiple rule and the derivative of cosine. The constant multiple rule allows us to take the constant (π/3) out of the differentiation process. The derivative of cos(θ) with respect to θ is -sin(θ).

The derivative of the function is therefore:

y' = -(π/3) sin(θ)

This means that for any value of θ, the rate at which y changes is -(π/3) times the sine of θ.