find the first derivative of y=cos(/9t+11
To find the first derivative of the function y = cos(θ) where θ is any expression, in this case (/9t+11), you can apply the chain rule. The chain rule states that if you have a composition of functions, you can compute the derivative by multiplying the derivative of the outer function with the derivative of the inner function.
Let's break it down step by step:
Step 1: Identify the inner function.
In this case, the inner function is (/9t+11).
Step 2: Find the derivative of the inner function.
The derivative of t with respect to t is 1, and the derivative of a constant (such as 11) is 0. Therefore, the derivative of the inner function (/9t+11) is 1/9.
Step 3: Find the derivative of the outer function.
The derivative of cos(θ) is -sin(θ).
Step 4: Multiply the derivative of the outer function with the derivative of the inner function.
Using the chain rule, we have: -sin(/9t+11) * (1/9).
Therefore, the first derivative of y = cos(/9t+11) is:
dy/dt = -sin(/9t+11) * (1/9).
Remember to simplify or rearrange the equation as needed.