Derivatives -Basic Rules to Product rule

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

• y = 2x + 1 - 3x^-1

• y' = 4x + 1 - 1x^-2

• y' = 2 + 3x^-2

• y' = 4x + 1 - 3x^-2

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

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

Tags

CCSS.8.EE.B.5

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

The derivative of 

• y'=2x-x^-2
• y'=x^-1+8x
• y'=x^-2+8x
• y=8x-x^-2

f(x)= 9/∛x
f'(x) =

• 9x^-1/3
• -3x^-4/3
• -9x^2/3
• -3x^2/3

Tags

CCSS.HSF-BF.B.4A

Differentiate h(x) = 3x^5/3 - 6x^1/6 + 3x

• h'(x) = 5x^2/3 - x^-5/6 + 3

• h'(x) = 3x^2/3 - 6x + 3

• h'(x) = 5x^4/3 - 6x + 3

• h'(x) = 3x^4/3 - x^-5/6 + 3

• 3x^2 – x
• x^3 + x^2 + x
• 3x^2

Tags

CCSS.HSF-IF.C.7C

 $f\left(x\right)=\left(-10x^2-7x^{\frac{2}{5}}+9\right)\left(2x^3+4\right)$  

•  $10x^4+\frac{238x^{\frac{2}{5}}}{5}-54x^2+80x+\frac{56}{5x^{\frac{3}{5}}}$  

•  $100x^4+126x^2+18-\frac{60}{x^3}$  

•  $10x^4-\frac{238x^{\frac{2}{5}}}{5}+54x^2-80x-\frac{56}{5x^{\frac{3}{5}}}$  

•  $60x^4-\frac{148x^{\frac{2}{5}}}{5}+28x^2-14x-\frac{36}{7x^{\frac{3}{5}}}$  

Tags

CCSS.HSA.APR.A.1

What is the derivative of csc(x)?

• csc(x)cot(x)
• -csc(x)cot(x)
• -csc²(x) 
• -cot²(x)

Find the derivative of f(x) = x²sinx

• f'(x) = 2xsinx - x²cosx
• f'(x) = 2xsinx + x²sinx
• f'(x) = 2xsinx + x²cosx
• f'(x) = 2xcosx