Question

calculate the derivative of the following function.
y = cos(11t + 4)
$\frac{dy}{dt}=square$

Explanation:

Step1: Identify the outer - inner functions

Let $u = 11t+4$, then $y=\cos(u)$.

Step2: Find the derivative of the outer function

The derivative of $y = \cos(u)$ with respect to $u$ is $\frac{dy}{du}=-\sin(u)$.

Step3: Find the derivative of the inner function

The derivative of $u = 11t + 4$ with respect to $t$ is $\frac{du}{dt}=11$.

Step4: Apply the chain - rule

By the chain - rule $\frac{dy}{dt}=\frac{dy}{du}\cdot\frac{du}{dt}$. Substitute $\frac{dy}{du}=-\sin(u)$ and $\frac{du}{dt}=11$ into it. Replace $u$ with $11t + 4$. So $\frac{dy}{dt}=-11\sin(11t + 4)$.

Answer:

$-11\sin(11t + 4)$