Test 2 Derivatives Review

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

The derivative of 

• y'=2x-x^-2
• y'=x^-1+8x
• y'=x^-2+8x
• y=8x-x^-2

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx

When you plug a given point into the derivative of a function, you get this.

• tangent line

• normal line

• slope

• average rate of change

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2

• 3(x²+2)/(x²+2)²

• (-3x²+4x +6)/(x²+2)²

• (-3x²+10)/(x²+2)²

Find the derivative of y = x⁴⋅cos x

• y' = x⁴ cosx - 4x³sinx

• y' = 4x³ cosx - x⁴sinx

• y' = 4x³ cosx + x⁴sinx

• y' = -4x³cosx

Find the derivative f(x) = tanxcosx

• f'(x) = sec²xcosx - tanxsinx
• f'(x) = sec²xcosx + tanxsinx
• f'(x) = sec²xsinx
• f'(x) = sec²xcosx - tanxcosx

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

• cusp, horizontal tangent, discontinuity
• cusp, vertical tangent, continuity
• cusp, vertical tangent, discontinuity
• curve, vertical tangent, continuity

• position
• velocity
• acceleration
• total distance

• position 
• velocity
• acceleration
• total distance