Differentiation

Find the derivative of
 $f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$  

•  $-2x^2-x+9$  
  

•  $-2x^3-x^2+9x$  
  

•  $-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$  
  

•  $-2x^4-x^3+9x^2$  
  

Differentiate y =  $\frac{12}{x^2}$  

• y' = 24x^-1

• y' = -24x^-3

• y' = -24x^-1

• y' = 6x^-3

Find the derivative of the funtion. (hint: you will need to multiply first!)

• 4x⁸+60x⁶+12x³

• 12x⁷+36x²

• 32x⁷+36x²

• 20x⁶

Find the fully simplified Derivative of y = 4x² + 3x + 6x^-2

• y' = 8x + 3 -12x^-3

• y' = 8x + 3 +12/x³

• y' = 8x + 3 -12/x³

• y' = 8x + 3 + 12/x

Find the slope at x = 3 of the equation f(x) = 3x²

• 6x

• 27

• 18

• 3x

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 6x(x² + 1)²
• dy/dx = 2x(x² + 1)²

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)
• f '(x) = 30x⁶(x⁶ + 4)

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = 168x⁶(5+8x)²
• f '(x) = 24x⁷(5+8x)²+7x⁶(5+8x)³
• f '(x) = 3x⁷(5+8x)²+7x⁶(5+8x)³
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Choose the correct answer

• $\frac{3}{2}$

• $\frac{-3}{2}$
  

• $\frac{7}{2}$

• $\frac{-7}{2}$