Derivative Rules (including chain rule)

Find the derivative of  f(x) = (x⁶ + 4)⁵

• f '(x) = 5x⁵(x⁴ + 4)⁴
• f '(x) = 6x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁵(x⁶ + 4)⁴
• f '(x) = 30x⁶(x⁶ + 4)⁴

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

find y' for y=(e^5x)+1

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Tags

CCSS.HSF-IF.C.8B

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Differentiate:

f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)

• f '(x) = 24x⁷ (5 + 8x)² +7x⁶(5 + 8x)³

• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Find the derivative of the given equation
f(x) = 1/x²

• 1/2x
• -2x
• 2x
• -2x^-3

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

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

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$  

•  $-3x^2+12x^3$  

•  $-21x^3+6x$  

•  $-21x^6+6x^2$  

•  $-84x^6-6x^2$  

Use the product rule to determine the derivative.

• 4x⁸+60x⁶+12x³
• 12x⁷+36x²
• 32x⁷+36x²
• 20x⁶