Download Unit 4 Review Sheet - Little Miami Schools

CALCULUS A
REVIEW OVER
4.1 – 4.4
Know the power, product and quotient rules of differentiation.
Know the Chain Rule and the Power Chain Rule.
1. y = sin(7 - 5x)
3
4
2. y = x (2 x  5)
3. y  (sin( 4 x)) 3
4. y =
5
(3x  3)
Understand and know how to use Implicit Differentiation to solve for
dy/dx.
3
4
5. x  y  2xy
Find dy/dx and
d2y
dx 2
2
6. y  2y  2x 1
Find dy/dx. Set this problem up but do not simplify.
7. x 2 
(x  y)
(x  y)
Find the derivatives of inverse Trigonometric functions using
identities and
rules given.
1
8. y = tan (3t  7)
9. cot 1 3x  1
1
10. y  sin (3x)
11. y  sec 1
x
(1  x)
Find the derivatives of exponential and logarithmic functions.
12. Y = x 4 (e x1 ) 
13. Y = 7 (x
x
5
3 5x)
2
14. Y = ln( x  8)
15. Y = log 5 (3x 4 )
16.
The amount of A (in grams) of radioactive plutonium remaining in a
20 gram sample after t days is given by the formula
A = 20(.5)
t
140
At what rate is the plutonium decaying when t = 6 days? Answer in
appropriate units.
17. A function f and its first and second derivatives are defined for all real
numbers, and it is given that f(0) = 2, f’(0) = 3, and f”(0) = -1.
a. Define a function g by g(x) = e kx  f (x) where k is a constant.
Find g’(0) and g”(0) in terms of k. Show your work.
b. Define a function h by h(x) = cos(bx)f(x), where b is a constant.
Find h’(x) and write an equation for the line tangent to the graph h at
x= 0.