Test Chap 15
7 March 2018
Name: _______________________________________________
Find the derivative of each function (Questions 1 -7)
dy
or y¢
dx
Don't forget to rewrite the function first (if possible) in order to make differentiation easier.
Use proper notation throughout. Don’t worry if you use
1.
y = 4x3 - 2x2 + 3x -1
2.
y = ( 2x - 3) ( x + 4 )
3.
f (x) =
4.
g( x) = -2ln ( 3x - 5 )
5.
f (x) = esin x cos2x
6.
e2 x
y=
x
7.
f (x) = ln x 2 - 3x
8.
y=
9.
Find the gradient of the tangent to y = e2 x +10 at x = ln 3
10.
f (x) = ekx + x and f ¢ ( 0 ) = -8 Find k
2x3 - x2 + 4x - 2
x
(
e2 x + 2
3e-2 x + 4
)
Show that
dy 12 + 8e2 x +12e-2 x
=
2
dx
( 3e-2 x + 4 )
(This is straight off a Homework Healthcheck!)
(This is straight off a Homework Healthcheck!)
1
Free Plain Graph Paper from http://incompetech.com/graphpaper/plain/