Calculus Final Review Test 1 (Unit 9-12)

• d/dx (tan(x))

  sec^2(x)
• If n E R & f(x) = x^n, then f'(x) = nx^(n-1)
• d/dx (f(x) +/- g(x)) =

  d/dx f(x) +/- d/dx g(x)
• A line is normal to a curve at a point if it is perpendicular to the tangent line at that point
• Two lines are perpendicular if and only if the slope of one line is the negative reciprocal of the other
• Tangent Line Equation example

  y + 6 = -1/5(x+1)
• Normal line Equation example

  y + 6 = -1/5(x+1)
• How to find where a function has horizontal tangents?

  Find where does the derivative equal to 0
• Product Rule

  d/dx (f(x)g(x)) = f'(x)g(x) + g'(x)f(x)
• Quotient Rule

  d/dx (f(x)/g(x)) = f'(x)g(x) - g'(x)f(x) / (g(x))^2
• (fg)'a means

  d/dx [ f(x)g(x) ] evaluated at x=a
• d/dx (sin(x)) = cos(x)
• d/dx (cos(x)) = -sin(x)
• d/dx (csc(x)) = -csc(x)cot(x)
• d/dx (sec(x)) = sec(x) tan(x)
• d/dx (cot(x)) = -csc^2(x)
• d/dx (a^x) = a^x * ln(a)
• d/dx (a^f(x)) = a^f(x) * ln(a) * f'(x)
• Chain rule

  f'(g(x)) * g'(x)
• d/dx(e^f(x)) = e^f(x) * f'(x)