Ch10 The Calculus

Power Rule

100

Find the derivative

y = 6x² - 8x³

dy/dx = 12x - 24x²

200

Find the derivative

y = 7x^-3

dy/dx = -21x^-4

300

Find the derivative

f(x) = 25/x

f'(x) = -25x^-2

400

Find the derivative

f(x) = x^5/2

f'(x) = 5/2x^3/2

or  2.5x^1.5

500

Find the derivative, and simplify completely.

f(x) = 4(x-8)³

12x² - 192x + 768

Chain Rule

100

Find the derivative

y = -8e^5x

-40e^5x

200

Find the derivative.

y = ln(-3x+4)

-3 / ln(-3x+4)

300

Find the derivative. 

y = (4x+9)^1/2

2(4x+9)^-1/2

400

Find the derivative.

y = 2ln(x^1/4)

1/2x

500

Find the derivative.

y = 5(lnx)³

15/x(lnx)²

Slope of Tangent/Normal

100

Find the slope of the tangent line to the graph of y = 6x³+2x at the point when x = 1

20

200

Find the slope of the tangent line to the graph of y = -4x^-1 at the point when x =2

1

300

Find the slope of the normal line to the graph of y = 6/x at the point when x =6

6

400

Find the slope of the normal line to the graph of y = x^1/2 +x at the point when x =1

-2/3   or  -0.6666666666

500

Find the slope of the tangent line to the graph of y =(5x+9)(4x-7) at the point when x =8

321

Final Jeopardy

500

Let f(x) = 5kx³ + 3kx² - 8kx, and it is known that f'(2) = 5. Find the value of k. Write your answer as a reduced fraction.

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