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Review Logarithms and exponentials Flashcards | StudBud

Explore/Review Logarithms and exponentials

Review Logarithms and exponentials

11 terms·StudBud Administration·10 plays

Review of Derivatives and Integrals involving logarithmic and exponential functions (chain rule also included)

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Questions 11

Answers

1
Find the derivative: y = ln(2x² + 3)
y' = (-2x2 + x - 2)/[(2x2 + 3)(x + 1)]
y' = 4x/(2x2 + 3)
y' = 1/(2x2 + 3)
y' = (2x2 + 3)/[ln(2x2 + 3)]
2
Find the derivative: y = 2^x· ln x
y' = 2x/x + 2xlnx
y' = 2xlnx + (ln2)2xlnx
y' = (ln 2)2x / x
y' = 2x/x + (ln2)2xlnx
3
Find the integral: ∫ e^{4x^6}x⁵dx
(1/24)e4x^6
(1/6)e4x^6 x6 + C
(1/5)e4x^6 + C
(1/24)e4x^6 + C
4
Solve ln(x-2)=lnx - 2
2.451
-4.780
2.313
2.890
5
Solve e^3x+1 = 8
3.61
0.791
1.03
0.360
6
Find the derivative: y = e^{5x - 11}
y' = 5e5x - 11
y' = e5
y' = (ln5)e5x - 11
y' = e5x - 11
7
Find the integral ∫2/(1-4x)
-0.5ln(1-4x)
2ln(1-4x)
ln(1-4x)
-2ln(1-4x)
8
Simplify log8 + log2 - log4
2log2
log8
2log4
log4
9
Find the integral: ∫ (6x⁴- 14x³+ 4x)/(2x²) dx
(6/5)x5- (7/2)x4 + 2x2
x3 - (7/2)x2 + 2lnx
6x - 7 + (2/x2) + C
x3 - (7/2)x2 + 2lnx + C
10
Find the derivative: y = ln(3x² + 5x - 2)
y' = ln(6x + 5)
y' = (3x2 + 5x - 2)/(6x + 5)
y' = (6x + 5)
y' = (6x + 5)/(3x2 + 5x - 2)
11
Find the integral: ∫ (2x² - 4x + 5)/(2x³- 6x²+ 15x - 23) dx
(1/3)ln(2x3 - 6x2 + 15x - 23) + C
(1/3)ln(2x2 - 4x + 5)+ C
ln(6x2 - 12x + 15) + C
ln(2x3 - 6x2 + 15x - 23) + C