Review of Differentiation

Find the derivative of f(x) = 5x² + 7x - 3.

• 2x + 7
• 10x + 7
• 10x + 4
• 2x + 4

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

.

• Only the Chain Rule
• The quotient & the Chain Rules
• Only the Quotient Rule
• Product & Quotient Rules

Find the derivative:
y=5x²e^3x

• y'=10xe^3x(2x+3)
• y'=5xe^3x(3x+2)
• y'=10ex^3x(3x+2)
• y'=5xe^3x(2x+3)

The derivative of xcos(2x²)

• cos(2x²) - 4x²sin(2x²)
• sin(2x²) - 4x²cos(2x²)
• cos(2x²) + 4x²sin(2x²)
• cos(2x²) - 2x²cos(2x²)

Calculate the gradient of f(x)=ln(x)+x at x=2/3

• 0.261

• 2.5

• 1.5

• -0.405