Differentiate the functions with respect to x in Exercises 1 to 8. 1. sin (x2 + 5) 2. cos (sin x) 3. sin (ax + b) 4. sec (tan ( x )) 5. sin ( ) cos ( ) ax b cx d + + 6. cos x3 . sin2 (x5) 7. ( 2 ) 2 cot x 8. cos ( x ) 9. Prove that the function f given by f (x) = | x 1|, x R is not differentiable at x = 1. 10. Prove that the greatest integer function defined by f (x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
Question 1:sin (x2 + 5)
Question 2:cos (sin x)
Question 3:sin (ax + b)
Question 4:sec (tan ( x ))
Question 5:sin ( ) cos ( ) ax b cx d + +
Question 6:cos x3 . sin2 (x5)
Question 7:( 2 ) 2 cot x
Question 8:cos ( x )
Question 9:Prove that the function f given by f (x) = | x – 1|, x Î R is not differentiable at x = 1.
Question 10:Prove that the greatest integer function defined by f (x) = [x], 0 < x < 3 is not differentiable at x = 1 and x = 2.
