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ln(x)
e^x
a^x
L'Hopital
etc.
100
∫
1
x
1/t dt
ln(x)
100
y= e
x
3
. Find y'.
y' = 3x
2
e
x
3
100
y=7(4)
x
. Find y'.
y' = 7ln(4)4
x
100
lim
x→∞
(3x
5
+2)/(7x
5
-8)
3/7
100
y=log
7
(8x). Find y'.
y'=1/xln(7)
200
y= √ (3x
3
+5x). Find y'.
y'=(9x
2
+5)/(2(3x
3
+5x)
1/2
)
200
y=e
-5x
2
cos(x). Find y'.
y'=-10xe
-5x
2
cos(x)-e
-5x
2
sin(x)
200
y=8
x
/e
x
. Find y'.
y'=(8
x
/e
x
)(ln8-1)
200
lim
x→0
(e
3x
)/(x
2
)
∞ (not L'Hopital)
200
d/dx[∫
4
x
sin√t dt]
sin(√x)
300
y= ln(x sin(x)). Find y'.
y' = 1/x +cot(x)
300
∫xe
5x
2
dx
1/10e
5x
2
+C
300
∫(12)
3x
dx
1/3ln(12)12
3x
+C
300
lim
x→0
(x
2
)/(cos(3x)-1)
-2/9
300
y=(10x)
cos(x)
. Find y'.
[-ln(10x)sin(x)+cos(x)/x](10x)
cos(x)
400
∫(tan√x)/(√x) dx
-2ln|cos√x|+C
400
∫(e
x
+4)
2
dx
1/2e
2x
+8e
x
+16x+C
400
∫(5x)/(7)
x
2
dx
(-5/2ln(7))(7)
x
2
+C
400
lim
x→∞
(e
x
)/(e
5x
)
0
400
d/dx[∫
-2
5x
e
t
2
dt]
5e
25x
2