Question

find the derivative of $f(x)$. $f(x)=2\sin(x)-2\cos(x)$ $f(x)=$

Explanation:

Step1: Recall derivative rules for sin and cos

The derivative of $\sin(x)$ is $\cos(x)$, and the derivative of $\cos(x)$ is $-\sin(x)$. Also, the derivative of a constant multiple of a function is the constant multiple of the derivative of the function.

Step2: Differentiate each term

For the first term $2\sin(x)$, its derivative is $2\times\frac{d}{dx}[\sin(x)] = 2\cos(x)$.
For the second term $-2\cos(x)$, its derivative is $-2\times\frac{d}{dx}[\cos(x)]=-2\times(-\sin(x)) = 2\sin(x)$.

Step3: Combine the derivatives

Adding the derivatives of the two terms together, we get $f^\prime(x)=2\cos(x)+2\sin(x)$.

Answer:

$2\cos(x) + 2\sin(x)$