Differentiation 2

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

Tags

CCSS.HSF-BF.B.4A

d/dx (sin²x) = ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

Find dy/dx for
(3x - 2x²)³

• dy/dx = (3 - 4x)⋅3(3x - 2x²)²
• dy/dx = 3(3x - 2x²)²
• dy/dx = 3(3 - 4x)²
• dy/dx = (3 - 4x)(9x - 18x²)²

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)

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)

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)

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 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 derivative of the function h(t) = t⁴ - (t⁴ - 1)⁸ ?

• h^'(t)= 4t³ - 8t³(t⁴ - 1)⁸

• h^'(t)= 4t³ - 32t³(t⁴ - 1)⁷

• h^'(t)= 4t³ - 8(t⁴ - 1)⁷

• h^'(t)= 4t² - 32t³(t⁴ - 1)⁸

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)