derivatives product quotient chain rule

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

find 

• y = 2 x^-1
• y=2 x^-2
• y= −2x^-2
• y= −2 x^-1

Tags

CCSS.HSF-IF.C.7A

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

What is the derivative of sin(x)?

• -sin(x)
• -cos(x)
• cos(x)
• sin(x)

Which of the following is the derivative of g(x)= (x²)(2x⁴ + 2)⁵ ?

• g^'(x)= (2x)(2x⁴ + 2) ⁵ + (x²)(5(2x⁴ + 2)⁴(8x³))

• g^'(x)= 2x + 8x³

• g^'(x)= (2x)(2x⁴ + 2)⁵ + (x²)(8x³)

• g^'(x)= (2x)(5(2x⁴ + 2)⁵(8x³)) + (x²)(2x⁴ + 2)

Which of the following is the quotient rule for derivatives?

• h^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))

• h^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))

Which of the following is the derivative of the function h(x)= (8x⁶ + 2x + 5)^{4 ?}

• h^'(x)= 4(8x⁶ + 2x + 5)³(48x⁵ + 2)

• h^'(x)= 4(48x⁵ + 2)³

• h^'(x)= 4(48x⁵ + 2 + 5)³

• h^'(x)= 3(8x⁶ + 2x + 5)⁴(48x⁵ + 2)²

Which of the following is the chain rule for derivatives utilizing the original function h(x) = f(g(x))

• h^'(x)=(f^'(g(x))(f^'(x))

• h^'(x)=(f^'(g(x))(g(x))

• h^'(x)=(f^'(g(x))(f(x))

• h^'(x)=(f^'(g(x))(g^'(x))

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4