Basic Derivatives

Which if the following is not a correct notation for 'derivative?'

• f'(x)
• y'
• dy
• dy/dx

Find g'(x) if g(x)=4x³

• 12x³
• 4x²
• 3x⁴
• 12x²

If q(x)=(3x-5)⁴, what is q'(x)?

• 4(3x-5)⋅3
• 4(3x-5)³⋅3
• 4(3x-5)
• 4(3x-5)³⋅

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

Tags

CCSS.HSA.REI.D.11

CCSS.HSF.IF.C.7

If f(x)=(6x²-5x)⁷
what is f'(x)?

• 7(6x²-5x)⁶
• 7(6x²-5x)⁶⋅(12x)
• 7(6x²-5x)⁶⋅(12x-5)
• (12x-5)

 $f\left(x\right)=\frac{5}{x^2}$  

f'(x) = 

• 5x

• 5/2x

• 5x^-2

• -10/x³

Tags

CCSS.HSA.APR.D.7

Differentiate y = (2x² + x - 3) / x

• y = 2x + 1 - 3x^-1

• y' = 4x + 1 - 1x^-2

• y' = 2 + 3x^-2

• y' = 4x + 1 - 3x^-2

Use the quotient rule to differentiate.

 $P\left(s\right)=\frac{7s}{s^3+4}$  

•  $P'\left(s\right)=\frac{7\left(4+2s^3\right)}{\left(s^3+4\right)^2}$  

•  $P'\left(s\right)=-\frac{7\left(4+4s^3\right)}{\left(s^3+4\right)^2}$  

•  $P'\left(s\right)=-\frac{7\left(4+3s^3\right)}{\left(s^3+4\right)^2}$  

•  $P'\left(s\right)=-\frac{7\left(-4+2s^3\right)}{\left(s^3+4\right)^2}$  

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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)

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.SSE.A.2

Find the derivative of y = 2x² (3x - 4)

• 6x³ - 8x²
• 18x² - 16x
• 15x² - 6x
• 6x - 4

Tags

CCSS.HSA.SSE.A.2