Derivatives Quiz 5

d/dx (sin³(4x^-6)) = ?

• -24x^-5 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ cos (4x^-6) ⋅ 3sin²(4x^-6)
• -24x^-7 ⋅ 3cos²(4x^-6)
• 3cos²(-24x^-5)

Find y' if y = tan(3x²+2).

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

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.IF.A.2

Find dy/dx if y = sec(8x²).

• sec(16x)tan(16x)
• 16xcos(8x²)
• 16xsecxtanx(8x²)
• 16xsec(8x²)tan(8x²)

Find the derivative f(x) = tanxcosx

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

Tags

CCSS.HSF.IF.C.8

Find the derivative of  $x^2+xy+y^3=0$  

•  $-\ \frac{2x}{1+3y^2}$  

•  $-\frac{x+3y^2}{2x+y}$  

•  $-\frac{2x+y}{x+3y^2}$  

•  $-\frac{2x}{x+3y^2}$  

Differentiate:

f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)

• f '(x) =24x^7(5+8x)^2+7x^6(5+8x)^3

• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Find  $\frac{dp}{dq}\ if\ p=\frac{1}{\sqrt{q+9}}$  

•  $-\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

•  $\frac{1}{2\left(q+9\right)^{\frac{3}{2}}}$  

•  $-\frac{1}{\left(q+9\right)^{\frac{3}{2}}}$  

•  $-\frac{1}{\sqrt{q+9}}$  

Tags

CCSS.HSN.RN.A.2

Find the derivative.

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

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.TF.A.2

Find the derivative.
y = x² / (3x-1)

• y' = 9x² - 12
  y' = (3x-1) / (3x-1)²
• y' = (3x² - 2x) / (3x-1)²
• y' = (6x+1)² / 3

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