Basic Derivatives
What is the derivative of y = 3x2? Name the rule used.
y' = 6x; power rule!
This function is the derivative of y = 3x2 * (7x+2).
What is y' = 63x2 + 12x? FROM:y'=3x2(7)+(7x+2)(6x)
This is the value of y' if y = (3x - 9)4
What is 12(3x - 9)3?
(From 4 * (3x-9)3 * 3)
Find the derivative of y = ex.
What is y' = ex
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What is 사이-n?
Find the derivative of f(x) = 5. Name the rule used.
0; constant rule!
This function is the derivative of y = sin(x) * tan(x).
What is y' = sin(x) + tan(x)sec(x)? FROM: y' = cos(x) tan(x) + sin(x) sec^2(x). See GTA's shortcut for simplifying steps.
This would be the value of the derivative of y = sin(2x) at x = pi (radians).
What is 2? From y' = 2 cos(2x) and cos(2pi) = cos(0) = 1
f(x) = ln(x2)
What is 2/x?
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Who is 진실?
This common function is the derivative of y = sin(x).
What is y = cos(x)?
This common function is obtained if you use the quotient rule on the function y = csc(x).
What is dy/dx = -csc(x)cot(x)? FROM: y = 1/sinx, f = 1, g = sinx, (f'g - g'f)/g2 = (0 - cosx)/sin2(x) = -cos(x)/sin(x) * 1/sin(x) = -csc(x)cot(x).
This is y' if y = (9x2 + 4)1/3
What is (6x)/(9x2 + 4)2/3?
f(x) = 3x2
What is f'(x) = 2x ln3 3x2
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What is 새벽?
This function is the derivative of y= 1/2x3 + 4x2 - 1/3x.
What is y'= 3/2x2 + 8x - 1/3?
What is 1? FROM: f=x, g=x2+1, (f'g-g'f)/g2 = (x2+1 - 2x2)/(x2+1)2 at x = 0 is 1.
For the function f(g(x)), this is the value of f'(3) if f(3) = 3, g(3) = 3, and g'(3) = 3.
What is 9? (From: f'(g(x)) * g'(x) = f'(3) * 3 = 3 * 3 = 9)
f(x) = ln(4x4-9x)
What is f'(x) = [1/(4x4-9x)]*(16x3-9)?
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What is 눈?
These are the only two basic functions that are their own derivatives.
What are y = 0 and y = ex?
True or false: it is possible to use the product, chain, and quotient rule to differentiate the same function.
What is "true"? (Example: f(x) = (x sin(3x) / ex)
This constant would describe the instantaneous rate of change on the curve y = ln(2x) at all values of x.
What is ln(2)? From: y' = 1/(2x) * (ln|2| * 2x) = ln(2). OR ask GTA for the shortcut.
This is the function for which the derivative would be dy/dx = 3/x.
What is ln |3x|?
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