Home Library Explore SAT

Home Library Explore SAT

Derivatives of logs and exponential functions Flashcards | StudBud

Explore/Derivatives of logs and exponential functions

Derivatives of logs and exponential functions

11 terms·StudBud Administration·70 plays

Derivatives of exponential and logarithmic functions for business calculus

Flashcards11 cardsFPractice quizPHost liveL

Questions 11

Answers

1
Find dy/dx of y = 5^{(2x - 1)} log₃ (x² + 3) at x = 1
dy/dx = 1
dy/dx = 56.4
dy/dx = 22.58
dy/dx = 20
2
Calculate the derivative y = 6x/(2^x -1)
dy/dx = (6 - 6x(2xln(2))/(2x -1)
dy/dx = 6xln(2)/(2x -1)2
dy/dx = [6((2x -1) - 6x(2x ln(2))]/(2x -1)2
3
calculate the derivative of y = 7^x-2
dy/dx = 7x-2 ln(7)
y = 7x-3ln(7)
y = ln(7)/(x-2)
y = xln(7)
4
Calculate v'(25) for v(t) = 1547(1.083)^t
$19.84 billion/year
$19.84 trillion
$905 Billion
$19.84 Billion/year
5
Calculate the derivative y = log₆ (3x + 2)
dy/dx = 3ln(6)/(3x + 2)
dy/dx = 3/[ln(6)(3x + 2)]
dy/dx = 1/(ln(6)(3x + 2))
dy/dx = 3/(3x + 2)
6
Calculate the slope of the tangent line for the function y = 2^x, at x = 0
y = 2(2x + 1)
y = xln(2) + 1
y = 2x + 1
y = xln(2) - 1
7
Find the equation of the tangent line at x = 1 for y = log₂ x
y = 1/ln(2)(x - 1)
y = ln(2)x - 1
y = 1/ln(2)x - 1
y = 2x - 1
8
Calculate the derivative of y = log₂ x
y = ln(2)/x
y = 2/x
dy/dx = 1/ (xln(2))
y = xln(2)
9
Given N(t) = 8400 ln(t) - 10,500, find N(45)
Approximately 22.4 million
Can not be determined
Approximately $ 186.66 / year
Approximately 21.5 million
10
Given N(t) = 8400ln(t) - 10,500, find the rate of change when t = 45 years.
$186.67 per year
187 thousand non-farm proprietorship/year
187 non-farm proprietorship/year
$186.67 thousand per year
11
Find the derivative of y = 2^x
dy/dx = 2x ln(2)
dy/dx = 2(2x-1 )
dy/dx = 2x
dy/dx = 2(x-1)