Basic Derivative Information
The derivative calculates the ________.
What is the slope of the tangent line or the slope of the function?
d/dx [3x2]
What is 6x?
Define the Product Rule using p(x)q(x)
What is p′(x)q(x)+ p(x)q'(x)?
Define the Quotient Rule using p(x)/q(x)
[q(x)p′(x) - p(x)q′(x)]/(q(x))²
d/dx [tan x]
What is sec2x?
d/dx [5x4+8x3-x+1]
What is 20x3+24x2-1?
f(x)=x²sinx, find f′(x).
What is f′(x) = 2xsinx+ x²cosx?
Differentiate y= 2/(x+1)
What is y′ = -2/(x+1)²?
Differentiate y=csc(x)
What is y′ = -cot(x)csc(x)?
d/dx [linear function]
What is its slope?
d/dx [3/x]
What is -3x-2?
Differentiate y=3x³ex
What is y' = 9x2ex+3x3ex?
Given the position function s(t) = (3x+1)/(2x2) with distance in miles, find the velocity at t = 1 seconds. You must fully simplify your answer and include units.
What is v(1) = -5/2 miles/seconds?
Differentiate g(x) = -3cosx + cotx
What is g'(x) = 3sinx + -csc2x?
d/dx [5ex]
What is 5ex?
d/dx [5x-1/5+2x3/2]
You must simplify your answer and rewrite with no negative exponents.
What is -1/x6/5+3x1/2?
What is -1?
Write the equation of the tangent line to y = cos(x)/ex at x=0. Keep your answer in point-slope form.
What is y - 1 = -1(x - 0)?
d/dx [sin x/tan x]
What is (tan(x)cos(x)-sin(x)sec2(x))/tan2x?
The second derivative of position calculates...
What is the instantaneous acceleration?
d/dx [6/(3x2)3]
You must simplify your answer and rewrite with no negative exponents.
What is -4/(3x7)?
Given the position function s(t) = (3x+1)(2x2-1) with distance in miles, find the velocity at t = 2 seconds. You must fully simplify your answer and include units.
What is v(2) = 77 miles/seconds?
What is...?
Find the second derivative of y = tan(x) using product rule. You must simplify and combine your answer fully.
What is y'' = 2tan(x)sec2(x)?