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Chapter 8 Mini Calc Review (Logs and exponentials) Flashcards | StudBud

Explore/Chapter 8 Mini Calc Review (Logs and exponentials)

Chapter 8 Mini Calc Review (Logs and exponentials)

6 terms·StudBud Administration·20 plays

Review of Derivatives and Integrals involving logarithmic and exponential functions (chain rule also included) #calculus #derivatives #integrals #logarithms #exponentials

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Questions 6

Answers

1
Find the derivative: y = ln(3x² + 5x - 2)
y' = (6x + 5)/(3x2 + 5x - 2)
y' = ln(6x + 5)
y' = (3x2 + 5x - 2)/(6x + 5)
y' = (6x + 5)
2
Find the integral: ∫ e^{4x^6}x⁵dx
(1/6)e4x^6 x6 + C
(1/24)e4x^6
(1/5)e4x^6 + C
(1/24)e4x^6 + C
3
Find the derivative: y = e^{5x - 11}
y' = e5x - 11
y' = (ln5)e5x - 11
y' = e5
y' = 5e5x - 11
4
Find the derivative: y = 2^x · 5x⁴
y' = 2x(20x3) + 2x(5x4)
y' = 2x(20x3) - (ln5)(2x)(5x4)
y' = 2x(20x3) + (ln2)2x(5x4)
y' = (ln 2)2x(20x3)
5
Find the slope of the tangent to the graph of y = log₅x²at the point (8, 3)
0.0097
1.2424
0.1553
636.247
6
Find the derivative: y = 3^7x + 6x²
y' = 7(37x) +12x
y' = (ln3)217x +12x
y' = 7(ln3)37x +12x
y' = 217x +12x