Course: AP Calculus AB | Quiz: 18 | Instructor: D. Shubleka Name__________ No Calculators. Present neatly. Score_______.
1.
Find y' if y = ln ( x 2 + y 2 )
Your work:
Find y' if y = ln ( x 2 + y 2 )
dy
1 !
dy $
= 2 2 # 2x + 2y &
dx x + y "
dx %
dy
2y dy
2x
− 2 2
= 2 2
dx x + y dx x + y
dy !
2y $
2x
#1− 2 2 & = 2 2
dx " x + y % x + y
dy ! x 2 + y 2 − 2y $
2x
#
&= 2 2
2
2
dx " x + y % x + y
dy
2x
= 2 2
dx x + y − 2y
Course: AP Calculus AB | Quiz: 18 | Instructor: D. Shubleka Name__________ No Calculators. Present neatly. Score______.
1.
Find y' if ln xy = ysin x
Your work:
Find y' if ln xy = ysin x
1!
dy $
dy
# y + x & = y cos x + sin x
xy "
dx %
dx
1 1 dy dy
+
− sin x = y cos x
x y dx dx
$
dy ! 1
1
# − sin x & = y cos x −
dx " y
x
%
dy ! 1− ysin x $ xy cos x −1
#
&=
dx "
y
x
%
dy y ( xy cos x −1)
=
dx x (1− ysin x )