Determine whether the pairs of the functions are linearly inde- pendent or linearly dependent on the real line. f(x) = e^x sin(2πx), g(x) = e^x cos(2πx)

Use the Product Rule to differentiate the function. f(x) = = x° cos(x) f '(x) =

From a calculus perspective, a monotone function is a function whose derivative never changes sign. Which function below is a monotone function? y=arctan x 2 Oy = x : - x² Oy Oy = cos x y= |2x - 3|

Select one: O a. O b. O C O d. O e. dy dx Find the derivative for the function f(x) = cosx - 2ex dy dx dy dx dy dx = sinx – 2e* = -sinx - 2e* dy dx −sinx – 2xe*-1 = sinx . 2ex-1 = –sinx – 2xex