University:
University of North Dakota
Course:
Math 165 | Calculus I
Academic year:

2024
Views:

241

Pages:

1
Author:

otrhjko

Workshop #13 1. Compute the derivative of each of the following functions. (a) f (x) = x2 + tan(3x2 − x) (b) g(x) = sec(ex − x4 ) r x h(x) = 1+x (c) (d) j(x) = sin2 (3x + 1) (e) k(x) = x cos(2x) (f) l(x) = esin x sin(ex ) 2. Find an equation for the line that is perpendicular to the graph of f (x) = cos2 (x2 ) √ at π 1 , . 2 2 3. Differentiate the following. 2 (a) f (x) = sin x2 ex sin 2x 2 (b) g(x) = tan x + x 3 √ 3 (c) h(x) = sec ( x) (d) x3 ) j(x) = e(2e 4. Consider the function f (x) = 1 − x2 . We will compute the derivative of this function in two different ways. xex (a) Use the quotient rule to compute f 0 (x). (b) In f (x), rewrite the fraction as a product, then distribute and simplify. Now compute f 0 (x). (c) Which method did you prefer?