Use the rules of differentiation to find the derivative of the function.
y = π/2 cos(θ) − sin(θ)
y' = π/2 * (-sinθ) - cosθ
= -π/2 sinθ - cosθ
Why did the function go to the circus? To find its derivative, of course! Let's put on our clown shoes and get ready to differentiate.
To find the derivative of y = π/2 cos(θ) − sin(θ), we can use the rules of differentiation.
First, let's find the derivative of the cos(θ) term. The derivative of cos(θ) is -sin(θ), so our cos(θ) term will become -sin(θ).
Next, let's find the derivative of the sin(θ) term. The derivative of sin(θ) is cos(θ), so our sin(θ) term will become cos(θ).
Now, we can put it all together. The derivative of y = π/2 cos(θ) − sin(θ) will be:
dy/dθ = π/2 * (-sin(θ)) - cos(θ)
So, the derivative of the function is dy/dθ = -π/2 sin(θ) - cos(θ).
And there you have it! The function has taken a spin in the circus and its derivative is now ready to perform.
To find the derivative of the function y = π/2 cos(θ) − sin(θ), we can use the rules of differentiation. Here, θ is the independent variable.
The derivative of a constant multiplied by a function can be found by taking the derivative of the function and multiplying it by the constant. So, let's start by finding the derivative of cos(θ):
d/dθ (cos(θ)) = -sin(θ)
Next, let's find the derivative of sin(θ):
d/dθ (sin(θ)) = cos(θ)
Now, let's find the derivative of the function y = π/2 cos(θ) − sin(θ):
d/dθ (y) = d/dθ (π/2 cos(θ) − sin(θ))
Using the rules of differentiation, we can find that:
d/dθ (y) = π/2 * (-sin(θ)) - cos(θ)
Simplifying further, we get:
d/dθ (y) = -π/2 sin(θ) - cos(θ)
So, the derivative of the function y = π/2 cos(θ) − sin(θ) is -π/2 sin(θ) - cos(θ).
To find the derivative of the function, we can use the rules of differentiation.
The first step is to apply the derivative rule for trigonometric functions. The derivative of cos(θ) is -sin(θ), and the derivative of sin(θ) is cos(θ).
We also need to use the chain rule since we have a composite function involving θ. The chain rule states that if we have a function f(g(x)), then the derivative of f(g(x)) with respect to x is equal to f'(g(x)) multiplied by g'(x).
Let's find the derivative step by step:
1. Take the derivative of π/2 cos(θ):
- The derivative of π/2 cos(θ) is -π/2 sin(θ) since the derivative of cos(θ) is -sin(θ).
2. Take the derivative of -sin(θ):
- The derivative of -sin(θ) is -cos(θ) since the derivative of sin(θ) is cos(θ).
Therefore, the derivative of y = π/2 cos(θ) - sin(θ) with respect to θ is -π/2 sin(θ) - cos(θ).