Consider this function y = f(x) on the domain (-co, co). f(x) = { √x sin() + 38 if x = 0 38 if x = 0 (a) If x 0, f'(x)= | |

Consider the following functions. g(x) h(x) f(x) = x + Ex - 5x-2 x + √5x 5x 2 Find the derivative of each function. √5 = g'(x) 1+ 2√x h'(x) = 5 f'(x) = -4x-5√√5x (x) = -2√3 2x (5x-2)² X

Evaluate the first derivative of the following functions: g(x) : = cosx – sinx f (x) = 4x²cosx g(y) = 3siny – ycosy f(x) = 3secxtanx f(x) = 2 cos Vx - = 2 cos vx

2. Find the derivative of each function: cos (x) 1-x² (b) g(x) = 5³√x - (a) f(x): (c) f(x) = (3x² + x − 12)(7x² − 4x) - (d) s(t) = 2t³ - 8t+4

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

Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) = + cos (x) In (3x)

3. Find f. (a) f"(x) = x + 12x? (b) f'(x) = cos x 3 (c) f'(x) = x² – x4 - A ch