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)= | |

Let Find f(x) a= -. y = f(x) = 5x + 18 cos x. d de f(x) = 7.

Find the derivative of the function. f(x) = 2xarccos(x) – 2/1 – x² X 2arccos(x) + 2 O 2arc cos (x) – 2/VI – x² os (x) – 2//1– x² 2arc cos (x) – 2x//1 – x² 2arccos(x)

f(x) = sin x In(5x)

Find f if f"(x) = sin x + cos x, f'(0) = 4, and f (0) = 9. Answer: f (x) =

Let f (x) = · cos(x). what is the correct result of the derivative of f with respect to x? =x. CoS A f'(x) =cos(x²) – 2x²sin(x²) in[ x B s'(x)=2x?sin(x²) + cos(x²) O s(x) =cos(x²) – xsin(x²) D f'(x) = – 2x²sin(x²)

Consider the function Suppose that g(6): f'(6) = f(x) = (1 + sin(x))9 (2) - 9 and g'(6) = − 4.

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

Show that

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