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# Calculus Rules

### Differentiation & Integration Rules

What is the integral of 1/x dx? ln|x| + C
What is the integral of e^x dx? e^x + C
What is the integral of x^5 dx? (x^6)/6 + C
What is the derivative of ln(x)? 1/x
What is the derivative of x^5? 5x^4
What is the derivative of logx? 1/(xln10)
What is the derivative of (3x + 7)^5? 15(3x + 7)^4
What is the derivative of xln(x)? ln(x) + 1
What is the derivative of (x + 5)/x? -5/x^2
What is the derivative of (x^2 + 5)/x? 1 - 5/x^2
What is the derivative of x/(x^2 - 1)? (-x^2 - 1)/(x^2 - 1)^2
What is the derivative of sin(x)? cos(x)
What is the derivative of cos(x)? -sin(x)
What is the integral of 2 dx? 2x + C
What is the integral of (x + 1)/x dx? x + ln|x| + C
What is the integral of x/(x + 1) dx? x + 1 - ln|x + 1| + C
What is the integral of sinx dx? -cosx + C
What is the integral of cosx dx? sinx + C
What is the integral of (3x + 2)^7 dx? ((3x + 2)^8)/24
What is the integral of 7^x dx? (7^x)/ln7 + C
How can the rate of change be found? Derive!
How can the area under a curve be found? Integrate!
What is the integral of (x^5 + 4x^3)/x? (x^5)/5 + (4x^3)/3 + C
What is the derivative of (9x^2 + 1)^4? 72x(9x^2 + 1)^3
How can the average value of f(x) = x^3 - 4 between x = 2 and x = 5 be found? 1/(5 - 2) * integral of x^3 - 4 from 2 to 5 using the Fundamental Theorem of Calculus
Solve ln(2 + x) = 5 for x. e^5 - 2
Solve log(3x - 1) = 7 for x. (10^7 + 1)/3 or 10000007/3
What is the inverse of y = 2x - 3? y = (x + 3)/2
What test is used to determine if an equation is a function? Vertical line test
What test is used to determine if a function has an inverse? Horizontal line test
What is the domain of lnx? Positive real numbers
What is the range of logx? All real numbers
If f(x) = 3x - 1, what is k if (k, 2) is on the inverse of f(x)? 5
Solve 5lnx = 2 e^(2/5)
What is ln1? 0
What is log1? 0
When using logarithmic differentiation as a tool, what type of logarithm is used? Natural logarithms! (The derivative of lnu = u'/u)
What is loga + 2logb simplified? log(a*b^2)
What is the value of "e" rounded to the nearest whole number? 3
How many derivatives must be taken of a polynomial with a degree of 23 before it equals 0? 24
Created by: mbarnard

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