Name: __________________
Class:
Date: _____________
(copy A)
1 Differentiate f (x ) = x cosx .
2 Differentiate y =
cotx + 1 .
cscx
(a) Find an equation of the tangent line to the curve y = secx 2 cos x at the point
3
(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.
a.
d.
b.
e.
c.
4 Differentiate.
PAGE 1
f(x) = x + 4 sin x
, 1 .
3
ANSWER KEY
Name: __________________
1.
2.
f'(x)=cos ( x ) x sin ( x )
x sin ( x ) +cos ( x )
f'=cos ( x ) x sin ( x )
cos ( x ) sin ( x )
y'(x)=cos ( x ) sin ( x )
cot ( x ) 1
csc ( x )
y'(x)= cot ( x ) 1
csc ( x )
sin ( x ) ( cot ( x ) 1)
y'(x)=sin ( x ) ( cot ( x ) 1)
PAGE 1
Class:
Date: _____________
3. y= 3 3 x+1 3
c
4.
df ( x ) =1+4cos x
( )
dx
1+4cos ( x )
(copy A)
Name: __________________
Class:
Date: _____________
1 Differentiate f (x ) = x cosx .
2 Differentiate y =
cotx + 1 .
cscx
(a) Find an equation of the tangent line to the curve y = secx 2 cos x at the point
3
(b) Illustrate part (a) by graphing the curve and the tangent line on the same screen.
a.
d.
b.
e.
c.
4 Differentiate.
PAGE 1
f(x) = x 7 sin x
2 , 1 .
3
(copy B)
ANSWER KEY
Name: __________________
1.
2.
f'(x)=cos ( x ) x sin ( x )
x sin ( x ) +cos ( x )
f'=cos ( x ) x sin ( x )
cos ( x ) sin ( x )
y'(x)=cos ( x ) sin ( x )
cot ( x ) 1
csc ( x )
y'(x)= cot ( x ) 1
csc ( x )
sin ( x ) ( cot ( x ) 1)
y'(x)=sin ( x ) ( cot ( x ) 1)
PAGE 1
Class:
Date: _____________
3. y=3 3 x 1 2 3
c
4.
df ( x ) =1 7cos x
( )
dx
1 7cos ( x )
(copy B)