Let f (x) = 6 sin x cos x. Choose the derivative of f: f'(x) = %3D O 12 sin? x O 12 cos? x 6 cos? x - 6 sin? x -6 sin x COS X 6 sin? x + 6 cos² x = 6(sin² x + cos? x) = 6 %3D

Q: Does the function cos x х f(x) = 0, x = 0 have a derivative at x = 0? Explain.

A:

Q: Differentiate the function. 8 + sin(t) f(t) cos(t) (a) f'(t) = Find f'(T). (b) f'(1) =

A: a:Here, f(t) =(8+sin(t))/cos(t)The derivative of f(t) is calculated as follows:

Q: Differentiate. f(x) = x cos(x) sin(x) (please write it out on paper)

A:

Q: If f(x) is a function of x, what is the derivative of f(sin(x))? f'(x) cos(f(x)) f'(x) cos(f'(x))…

A:

Q: Let f(x) = 9e* cos x f'(x) =

A: Given: f(x)=9excos x f'(x)=?   Solution: ddx(9excos x)

Q: Find the derivative of F(x) = 4 sin(t) dt. 3x %3D dx cos(x)

A: Solve the following

Q: 2 sin x f(x) = 2+ cos x find f' (x).

A: use ratio rule for finding the derivative of rational function.

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: If f(x) = 3x(sin x + cos x), find the derivative.

A:

Q: Let f(x) = – 7 cos(cos æ) %3| f'(x) =

A:

Q: Apply the Second-Derivative Test to find all relative extrema of the function  f(x)=cosx-x ,…

A:

Q: Let f(x) 3 sin(cos x) = f'(x) =

A: Using chain rule of differentiation.

Q: (b) Hint: sin(a + b) = sin(a) cos(b) + sin(b) cos(a) f (x) = sin(x) %3|

A: sin ( a + b ) =sin (a ) cos ( b ) + sin(b)cos(a)