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Differentiation & Integration Rules

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