Basic Differentiation Part 1

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Find the derivative of the given equation
f(x) = 1/x²

• 1/2x
• -2x
• 2x
• -2x^-3

Differentiate 6x^⅔.

• 4x^-⅓
• 4x^-⅔
• 6x^⅓
• 4x^⅓

Find the derivative of y = -sin x.

• y ' = -cos x
• y ' = cos x
• y ' = csc x
• y' = -csc x

If f(x) = cos x, find f'(x).

• f ' (x) = -cos x
• f ' (x) = sin x
• f ' (x) = -sin x
• f ' (x) = cos x

Find the derivative of:
f(x) = 2/x^0.5
hint: convert decimal to a fractional indice

• -1/x^1.5
• -2/x^1.5
• 2/x^1.5
• -2/x^0.5

• x⁵ + 5x⁴ + 2x³ + 6x² + 5
• 28x⁶ + 45x⁴ + 6x² + 40x
• 4x² + 8x + 1
• 4x⁷ + 49x⁵ + 50x³ + 20x² + 5

Given that the position function for a particular object is given by
s(t) = t³ - 3t +5, find the velocity of the object at t = 2 seconds. 

• 51
• 12
• 9
• 6

Given that the position function for a particular object is given by 
s(t) = t³ - 3t +5, find the acceleration of the object at t = 2 seconds. 

• 27
• 12
• 6
• -2

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx