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)= | |

Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax cos (bx) W' (x) =

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)

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 f(x) = 4 sin(x) cos(x) + 6 csc(x). Evaluate its derivative at the point x = 4π/3. Answer: f' (4π/3) = a a b √a |a| П sin (a) M

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

A2) Find the derivative of the following functions: x2 + 2 (a). f(x) x2 2 - (b). f(x) = 2 tan-1(x) – 3" (c). f(x) : = (x + 2 sin x) (1 – 8 cos x) tanx (d). g(x) = 2 – secx -

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

Verify that f′(x) = g′(x) and explain the relationship between f and g.

Find the anditerivative of the function f with the given condition f(x) = 0.5x8 - 4.5 sin(6.5x) and F(0) = -2. F(x) =