Basic Derivatives

Derivatives

100

Find the Derivative:

y = 5

y' = 0

200

Find the Derivative:

y = sqrt(x)

y' = 1 / (2x^1/2)

300

Find the Derivative:

y = 4x⁵ + x

y' = 20x⁴ + 1

400

Find the Derivative:

f(x) = 4x⁴ - 5x -3

f'(x) = 16x³ - 5

500

Find the Derivative:

y = -4x^-5 + 2x

y' = 20/x⁶ +2

More Derivatives

100

Find the Derivative:

y = 5x⁸

 y' =40x⁷

200

Find the Derivative:

y = 1/x²

y' = -2/x³

300

Find the Derivative:

y = x³ - 8x² +5

y' = 3x² - 16x

400

Find the Derivative:

y = 4x⁶ -7x⁵ -9x³ 

y' = 24x⁵ -35x⁴ -27x²

500

Find the Derivative:

y = 0.5x⁴ +5x + x^-3

y' = 2x³ + 5 - 3/x⁴

Product Rule

100

Define the Product Rule using f(x)g(x)

f′(x)g(x)+ g′(x)f(x)

200

Differentiate the Product

y=x^2(3x+1)

9x^2+2x

300

Differentiate 

(2x+1)(3x-2)

12x-1

400

Differentiate 

f(x)=(-3+x^-3)(-4x^3+3)

-9x^-4 -36x^2

500

Differentiate 

y=x^4(x^3-2x^2+3x-1)

7x^6-12x^5+15x^4-4x^3

Quotient Rule

100

Define the Quotient Rule using f(x)/g(x)

[g(x)f′(x) - f(x)g′(x)]/ (g(x))²

200

Differentiate y= 2/(x+1)

y′ = -2/ (x+1)²

300

Differentiate y= (1+lnx) / (x²-lnx)

y′= [(1/x)-x-2xlnx] / (x²-lnx)²

400

What is the derivative of a constant function?

Zero. Always. 

500

f(x)= (x²-1)³/ x²+1, what is f′(x)?

f′(x)= [4x(x²-1)²(x²+2)] / (x²+1)²

Potpourri

100

Two "boy bands" topped the charts for most album sales in 2000. Name one of those bands. 

'Nsync and The Beatles

200

Which Destiny's Child singer debuted her first single in 2000?

Beyonce

300

Who had a pet llama named Tina and voted for Pedro?

Napoleon Dynamite

400

This book was the final in its series when released in 2007, selling out all 15 million copies in under 24 hours. 

Harry Potter (and the Deathly Hallows)

500

What year was the World Wide Web introduced?

1989