AP CALCULUS BC
Section 5.1 - 5.2 - 5.4: Exponential and Logarithmic Functions: Differentiation and Integration
d x
e = ex
dx
d
1
ln( x) =
dx
x
∫
d x
a = a x ln(a )
dx
d
1
log a ( x) =
dx
x ln(a )
f ' ( x)
dx = ln ( f ( x) ) + C
f ( x)
Find the derivative of the following functions.
(You may use NDER to support your computations)
1.
y = x 2 e x − xe x
2.
y = x1+
2
 1 


 ln x 
3.
y=x
4.
y = ln(10 x )
AP CALCULUS BC
Section 5.1 - 5.2 - 5.4: Exponential and Logarithmic Functions: Differentiation and Integration
Find the derivative of the following functions:
1. f ( x ) = 2 x 2 e 4 x
 2 x 3x + 1 

2. g ( x) = ln
2

x


(
3. f ( x) = log 6 4 x 3 − 3 x
)
4. h( x) = ln sin x
5. g ( x) = −2 + e 3 x (4 − 2 x )
6. f ( x) = e 5 ln x
(
7. y ( x) = ln 5 2 x − 4
8. g ( x) = log 8
)
x2 − 3
2x
9. k ( x) = 3 4 x −1 + e 5 x
10. j ( x) = 5 sin( x )
Find
dy
dx
11. 2 x + 3 y = 4
13. y = (2 x + 1)
12. log10 cos x = 4 y
14. y = x arcsin( x )
x
AP CALCULUS BC
Section 5.1 - 5.2 - 5.4: Exponential and Logarithmic Functions: Differentiation and Integration
Integrate
1.
2.
3.
4.
5.
6.
7.
8.
9.
AP CALCULUS BC
Section 5.1 - 5.2 - 5.4: Exponential and Logarithmic Functions: Differentiation and Integration
MUST KNOW!
Let’s see where 9) and 10) above come from!