Name: __________________
1 Find the derivative of the function F (x ) =
Class:
( 3x 2
7x + 7
Date: _____________
)
3
.
2 Find the derivative of the function. Be sure to enclose all angles in parentheses.
y = e
2x
cos(5x)
x
3 Find the derivative of the function f (x ) =
3 .
5x
4 Find an equation of the tangent line to the curve y = 9 sin(sin(x )) at the point ( , 0 ) .
PAGE 1
(copy A)
ANSWER KEY
Name: __________________
Class:
Date: _____________
6 5x
3.
3
2
2 ( 3 5x )
6 5x
f'(x)=
2
f'(x)=
( 3 5x )
6 5x
2 ( 3 5x )
1
f'(x)=
+
3 5x
f'(x)=
1
+
3 5x
3
2
5x
2 ( 3 5x )
5x
2
df =
dx
( 3 5x )
3
3
6 5x
2 ( 3 5x )
6 5x
( 3 5x )
f'=
3
2
( 3 5x )
2
6 5x
f'=
2
3
3
3
6 5x
3
2
2 ( 3 5x )
df = 6 5x
dx
3
2
2 ( 3 5x )
5x
1
+
3
3 5x
2 ( 3 5x )
5x
df =
1
+
dx
3
3 5x
2 ( 3 5x )
5x
1
+
3
3 5x
2 ( 3 5x )
5x
1
f'=
+
3
3 5x
2
2 ( 3 5x )
5x
df
1
=
+
3
dx
3 5x
2
2 ( 3 5x )
5x
1
+
3
3 5x
2
2 ( 3 5x )
1
3 5x x
5
f'=
2 3 5x
3 5x
3 5x x
df =
dx
PAGE 1
1
2 3 5x
3 5x
5
(copy A)
ANSWER KEY
Name: __________________
Class:
Date: _____________
3 5x x
f'=
1
2 3 5x
3 5x
3 5x x
f'(x)=
2. y'(x)= e
y'= e
e
2x
PAGE 2
2x
2x
( 2cos ( 5x ) +5sin ( 5x ) )
( 2cos ( 5x ) +5sin ( 5x ) )
( 2cos ( 5x ) +5sin ( 5x ) )
4.
5
y= 9x+9
y ( x ) = 9x+9
y 9x 9 =0
1
2 3 5x
3 5x
5
(copy A)
Name: __________________
1 Find the derivative of the function F (x ) =
Class:
( 8x 2
5x + 4
Date: _____________
)
3
.
2 Find the derivative of the function. Be sure to enclose all angles in parentheses.
y = e
3x
cos(7x)
x
3 Find the derivative of the function f (x ) =
2 .
7x
4 Find an equation of the tangent line to the curve y = sin(sin(9x )) at the point ( , 0 ) .
PAGE 1
(copy B)
ANSWER KEY
Name: __________________
Class:
Date: _____________
4 7x
3.
3
2
2 ( 2 7x )
4 7x
f'(x)=
2
f'(x)=
( 2 7x )
4 7x
2 ( 2 7x )
1
f'(x)=
+
2 7x
f'(x)=
1
+
2 7x
3
2
7x
2 ( 2 7x )
7x
2
df =
dx
( 2 7x )
3
3
4 7x
2 ( 2 7x )
4 7x
( 2 7x )
f'=
3
2
( 2 7x )
2
4 7x
f'=
2
3
3
3
4 7x
3
2
2 ( 2 7x )
4 7x
df =
dx
3
2
2 ( 2 7x )
7x
1
+
3
2 7x
2 ( 2 7x )
7x
df =
1
+
dx
3
2 7x
2 ( 2 7x )
7x
1
+
3
2 7x
2 ( 2 7x )
7x
1
f'=
+
3
2 7x
2
2 ( 2 7x )
7x
df
1
=
+
3
dx
2 7x
2
2 ( 2 7x )
7x
1
+
3
2 7x
2
2 ( 2 7x )
1
2 7x x
7
f'=
2 2 7x
2 7x
2 7x x
df =
dx
PAGE 1
1
2 2 7x
2 7x
7
(copy B)
ANSWER KEY
Name: __________________
Class:
Date: _____________
2 7x x
f'=
1
2 2 7x
2 7x
2 7x x
f'(x)=
2. y'(x)= e
y'= e
e
3x
PAGE 2
3x
3x
( 3cos ( 7x ) +7sin ( 7x ) )
( 3cos ( 7x ) +7sin ( 7x ) )
( 3cos ( 7x ) +7sin ( 7x ) )
4.
7
y= 9x+9
y ( x ) = 9x+9
y 9x 9 =0
1
2 2 7x
2 7x
7
(copy B)