Basic Derivatives Review

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

At which point(s) will the slopes of the tangent line are zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

What is the equation of the line tangent to the curve y = x² at x = 1?

• y = 2x + 1

• y = 2x - 1

• y = -2x + 1

• y = x - 1

Find the slope at x = 3 of the equation f(x) = 3x²

• 6x

• 27

• 18

• 3x

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

• y+1=2(x+1)

• y=2x-1

• y=2x+2

• y= -x-1

• y = 2x + 1 - 3x^-1

• y' = 4x + 1 - 1x^-2

• y' = 2 + 3x^-2

• y' = 4x + 1 - 3x^-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

• 4x²+8x+1
• 20x⁶+5x⁴
• 28x⁶+5x⁴-16x

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 3(x² + 1)²(2x)
• dy/dx = 2x(x² + 1)²