cpcalc 3.3.3

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Find  $\frac{dy}{dx}\ if\ y=\frac{x^3}{x-1}$  

•  $\frac{2x^3-3x^2}{\left(x-1\right)^2}$  

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

•  $\frac{-2x^3-3x^2}{\left(x-1\right)^2}$  

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

Differentiate (2x + 2)(x - 5)⁸ with respect to x.

• (2x + 2)(x - 5)⁷ + 2(x - 5)⁸
• 8(2x + 2)(x - 5)⁷ + 2(x - 5)⁸
• 2(x - 5)⁸
• 16(x - 5)⁷

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• Only the Quotient Rule
• The Quotient and Product Rules
• The Quotient and Chain Rules
• Only the Chain Rule

Find the slope of the line tangent to the graph of $y=\sqrt{2x+1}$  at the point  $\left(4,\ 3\right)$  

•  $\frac{1}{3}$  

•  $\frac{2}{3}$  

•  $\frac{4}{3}$  

•  $\frac{1}{6}$  

Find $y'$ if  $y=10\left(\frac{x}{2x+1}\right)^5$   

•  $y'=\frac{50x^4}{\left(2x+1\right)^6}$  

•  $y'=\frac{50x^4}{\left(2x+1\right)^3}$  

•  $y'=\frac{50x^4}{\left(2x+1\right)^5}$  

•  $y'=\frac{-50x^4}{\left(2x+1\right)^4}$