Question

find $\frac{ds}{dt}$. s = 2tan t - $e^{-t}$ $\frac{ds}{dt}=$

Explanation:

Step1: Differentiate term - by - term

We know that the derivative of $\tan t$ with respect to $t$ is $\sec^{2}t$ and the derivative of $e^{-t}$ with respect to $t$ is $-e^{-t}$ according to derivative rules.

Step2: Apply constant multiple rule

The derivative of $2\tan t$ is $2\sec^{2}t$ (since the derivative of $cf(x)$ is $cf^{\prime}(x)$ where $c = 2$ and $f(t)=\tan t$). The derivative of $-e^{-t}$ is $e^{-t}$.

Answer:

$2\sec^{2}t + e^{-t}$