Find the integral: ∫ (2x2 - 4x + 5)/(2x3 - 6x2 + 15x - 23) dx

(1/3)ln(2x3 - 6x2 + 15x - 23) + C

Find the derivative: y = log3 (2x2 + 3)/(x + 1)

y' = (2x2 + 4x - 3)/[ln3(2x2 + 3)(x + 1)]

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Mixed Calculus Review (Logarithms and exponentials)

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

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Questions 14

Answers

1
Find the derivative: y = ln(3x² + 5x - 2)
y' = (6x + 5)
y' = (3x2 + 5x - 2)/(6x + 5)
y' = ln(6x + 5)
y' = (6x + 5)/(3x2 + 5x - 2)
2
Find the integral: ∫ x³(x⁴ - 7)⁶dx
(1/7)(x4 - 7)7 + C
(1/7)ln(x4 - 7)7+ C
(1/4)ln(x4 - 7)6+ C
(1/28)(x4 - 7)7 + C
3
Find the derivative: y = 3^7x + 6x²
y' = (ln3)217x +12x
y' = 7(ln3)37x +12x
y' = 7·37x +12x
y' = 217x +12x
4
Find the integral: ∫ 7^3xdx
(7x / 3ln7) +C
(73x / ln7) +C
(73x / 3ln7) + C
(73x / 3) +C
5
Find the integral: ∫ (2x² - 4x + 5)/(2x³- 6x²+ 15x - 23) dx
(1/3)ln(2x2 - 4x + 5)+ C
ln(2x3 - 6x2 + 15x - 23) + C
ln(6x2 - 12x + 15) + C
(1/3)ln(2x3 - 6x2 + 15x - 23) + C
6
Find the integral: ∫ e^{4x^6}x⁵dx
(1/24)e4x^6
(1/5)e4x^6 + C
(1/24)e4x^6 + C
(1/6)e4x^6 x6 + C
7
Find the derivative: y = (x⁵ -11)⁴
y' = 5x4(x5 -11)3
y' = 4(x5 -11)3
y' = 20x4(x5 -11)3
y' = 4(5x4)3
8
Find the integral: ∫ (6x⁴- 14x³+ 4x)/(2x²) dx
6x - 7 + (2/x2) + C
x3 - (7/2)x2 + 2lnx + C
x3 - (7/2)x2 + 2lnx
(6/5)x5- (7/2)x4 + 2x2
9
Find the derivative: y = log₃ (2x² + 3)/(x + 1)
y' = (-2x2 + x - 2)/[(2x2 +
y' = (-2x2 + x - 2)/[ln3(2x2 + 3)(x + 1)]
y' = (2x2 + 4x - 3)/[ln3(2x2 + 3)(x + 1)]
y' = (2x2 + 4x - 3)/[(2x2 + 3)(x + 1)]
10
Find the derivative: y = 2^x · 5x⁴
y' = 2x·20x3 + 2x·5x4
y' = (ln 2)2x·20x3
y' = 2x·20x3 - (ln5)2x·5x4
y' = 2x·20x3 + (ln2)2x·5x4
11
Find the equation of a tangent to the graph of y = log₅x²at the point (8, 3)
y = 0.0097x - 0.0776
y = 0.1553x - 1.2424
y = 0.0097x + 2.9224
y = 0.1553x + 1.7576
12
Find the derivative: y = e^{5x - 11}
y' = e5
y' = (ln5)e5x - 11
y' = e5x - 11
y' = 5e5x - 11
13
Find the area bounded by the following euquations: f(x) = x³(5^{-x^4}), y = 0, x = 0, x = 4
64.0387
-0.1335
0.1553
0.25
14
Find the derivative: y = 2^x· ln x
y' = 2x/x + (ln2)2xlnx
y' = (ln 2)2x / x
y' = 2xlnx + (ln2)2xlnx
y' = 2x/x + 2xlnx

Mixed Calculus Review (Logarithms and exponentials) Flashcards | StudBud