Power Rule Derivatives

Find the derivative of the given equation

f(x) = x⁴ + 4x³ - 2x²

• f'(x) = x³ + x² - x

• f'(x) = 4x³ + 12x² + 4x

• f'(x) = 4x + 12x - 4x

• f'(x) = 4x³ + 12x² - 4x

Differentiate  $y=\frac{2x^2+3x-4}{x}$  .

What is the slope of the tangent line to y = 4x⁴ - 7x³ + 0.5x² - 9 at x=1?

• 16x³ - 21x² + x

• 6

• 16x³ - 21x² + 0.5x - 9

• -4

Find the derivative of the funtion.

• 4x⁸+60x⁶+12x³

• 12x⁷+36x²

• 32x⁷+36x²

• 20x⁶

Differentiate

• $-3x+2x^{-\frac{1}{2}}$

• $-3x^{-2}+2x^{\frac{1}{2}}$

• $-3x^{-2}+2x^{-\frac{1}{2}}$

• $-3x^2+2x^{\frac{1}{2}}$

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

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

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

At which point(s) will the slope(s) of the tangent line be POSITIVE?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

Tags

CCSS.HSA-SSE.B.3B

CCSS.HSF-IF.C.8A

Find the fully simplified Derivative of y = 4x² + 3x + 6x^-2

• y' = 8x + 3 -12x^-3

• y' = 8x + 3 +12/x³

• y' = 8x + 3 -12/x³

• y' = 8x + 3 + 12/x

Tags

CCSS.HSA.APR.A.1

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

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