Derivatives 2 Review

When do you use the chain rule?

• when there is multiplication

• when there is a function in a function
• when there is division

.

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

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)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

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)

What is the derivative of e^x?

• xe^x-1
• x^e
• e^x
• e^x-1

Find the derivative f(x) = xe^x

• A. f'(x) = e^x

• B. f'(x) = xe^x + xe^x

• C. f'(x) = e^x - xe^x

• D. f'(x) = e^x + xe^x

Find the derivative:

y=(2^3x+4)

• 3(ln2)(2^3x+4)

• 3(2^3x+4)

• 3(2^3x+4/(ln2))

• 2^3x+4

Find the second derivative of
f(x) = x² + e^x  - cosx

• f"(x) = 2 + e^x + cosx
• f"(x) = 2x + e^x + cosx
• f"(x) = 2x + xe^x - cosx
• f"(x) = 2x + e^x + sinx

Find dy/dx by Implicit Differentiation 
x + 4y = 1

• -1/4
• -1 
• 4
• 1 

Find dy/dx by Implicit Differentiation
xy = 6

• -x/ y
• -y/ x
• -6y/ x
• y/x