Derivative Review Part 1

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Use the quotient rule to determine the derivative.

• 8x⁴ -60x²

• 16x⁴/(2x²-5)²

• (8x⁴ -60x²)/(2x²-5)²

• 3x

If f '(x) = 0, what does that mean with respect to the tangent line?

• Tangent line is vertical

• Tangent line has a positive slope

• Tangent line is horizontal

• Tangent line has a negative slope

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

Find the derivative of f(x) = x²sinx

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

Find the derivative of f(x) = -3x⁴cscx

• f'(x) = 12x³cscxcotx

• f'(x) = -3x⁴cscxcotx

• f'(x) =-12x³cscx + 3x⁴cotxcscx

• f'(x) = -3xcosx

y = (sinx)/x

find y’

• y' = (cosx)/x

• y' = (xcosx - sinx)/x²

• y' = (cosx - sinx)/x

• y' = (sinx - xcosx)/x²

Find dy/dx if y = cos⁵x

• 5cos⁴x
• -5sin⁴x
• 5cos⁴xsinx
• -5cos⁴xsinx