Math 125
Derivatives (Practice Test)
Mrs. Sandler
Name_________________________
Please think before doing, write exactly what you mean, show your work (the
answers without supportive work will worth nothing). Box or circle your answers. This
means: nothing boxed – no answer. Simplify the answers as much as possible. Make
sure your answers don’t have negative or fractional exponents or complex fractions.
Good luck!
1. Given
2. For
y  x  17 x  21x  5x  3 , find
5
3
2
 
f ( x)  sin 2 x , find f   .
2
3. Given
s  lnt 2e3t , find
ds
.
dt
5
d2y
.
dx 2
4.
du
4v 4  2v 3
Let u 
.
Find
.
dv
5v 2
5. For
g ( x)  ln 3x  4 , find g 2  .
6. For
y  23 x cosx    2 , find
dy
.
dx
7. For
h( x)  e 2 x  x , find h(x) .
8. Given
9. For
y  sin tan x  , find y .
H ( x)  x3 lncos x  , find H (x) .
10. For

f ( x )  ln x  x 2  a
11. Given
12. For

, find
f (x ) .
(3x  5) 2
, solve the equation: y   0 .
y
(4 x  1) 3
y  4 x  1 arctan( 2 x ) , find dy .
dx
13. For
dw
 2  3  1
, find
.
w
d
 1
14. For
y  e3ln x , find
dy
.
dx
15. Find an equation of the line tangent to
y
x
8  x 
2 5
at
x0  3 .