Derivatives!

Derivatives At a point

100

If f(x) = -3x²+5x+7, then f'(2) =?

f'(2) = -7

200

Find dy/dx at x = 1 for y = e^x-ex

0

300

Find the slope of the tangent line to the graph of 

2y-3x=7 when x = 42

slope is 3/2

400

Evaluate dy/dx at x = 4 given y = x^-1/2 - x^1/2

-5/16

500

g(x) = (x²+1)/(x-3), find g'(5)

x = -3/2

Trigonometric

100

Find dy/dx for y = tan(x/2)

dy/dx = 1/2 sec²(x/2)

200

find y' for y = x²/sinx

y' = (sinx)(2x) - x²(cosx) OVER sin²x

300

calculate f''(x) for f(x) = x³+sinx

f''(x) = 6x-sinx

400

y =  sin³x tan(3x) find y'. 

y' = sin³x sec²3x 3 + 3sin²x cosx tan3x

500

Find d²y/dx² for y = (cosxtanx), provide your answer in simplest form. 

-sinx

Chain RuLZ

100

Find the derivative of y = sin(sqrtx)

= cos(rootx)/(2rootx)

200

Find the instantaneous rate of change of 

y = (2+cos(x²))³

y' = 3(2+cosx²)²(-sinx²)(2x)

300

The velocity function for a particle traveling along the x axis if given by the equation v(t) = (t-3)(t²-1). Find the acceleration, v'(t), when t = -1/2. 

Give you answer in a reduced fraction. 

11/4 or 2 and 3/4

400

y = ln(e^{x^2}) find dy/dx at x = 1/3

2/3

500

Find the value of the second derivative when x = 2 and the curve is implicitly described by x³+xy=8. 

Zero

Graphs

100

SLIDE 1

Zero

200

SLIDE 2

-11/9

300

Slide 3

5, -1/2, true

400

Slide 4

Answers vary

500

Slide 5

The limit from the left of f'(x) as x ->1 is not the same as the limit from the right of f'(x) as x ->1 therefore f'(x) is not continuous at x = 1.