Practice Problems for Midterm 2
1)Dierentiate f (x) =
1+
1+
x.
2)Dierentiate f (x) = sin(tan( sin(x). 3)Write f (x) = cos3 ( 2ln(x) ) as a composition of 3 functions and then dierentiate f (x). x3 +1 4)Find y if sin(x + y ) = y 2 cos(x). 2 5)Find y if ln(
Math 1A
Calculus Prof. Haiman Practice Exam for Midterm 2Solutions
Fall, 2004
1. Dierentiate ex (cos x + sin x). 2ex cos x 2. Dierentiate ln( 873 sin x). (cot x)/2 3. Find
d3 (x3 dx3
ln x). 11 + 6 ln x
4. Dierentiate x(1/x) . x(1/x) x2 (1 ln x) 5. A table
Midterm 2 Solutions, Math 1A, section 1
Thursday, November 6, 2008, 8:10-9:30 am 1. Let p = 0. Show by implicit dierentiation that the tangent line to the curve xp + y p = 1, x > 0, y > 0
p at the point (x0 , y0 ) is given by the equation xp1 x + y0 1 y =
Math 1A, Calculus 1. Find
d2 (sec x). dx2
Second Midterm Exam Solutions
Haiman, Fall 2004
sec3 x + sec x tan2 x 2. Dierentiate x(e ) . 1 x x(e ) ex (ln x + ) x 3. If h(x) = f (g (x) and f (0) = 0, g (0) = 1, f (0) = 2, g (0) = 3, f (1) = 4, g (1) = 5, nd
Haiman
Math 1ACalculus Second Midterm Exam Solutions
Fall, 2006
Name Discussion Section (Time and GSI)
Student ID
You may use one sheet of notes. No other notes, books or calculators allowed. There are 8 questions, on front and back. Write answers on the