Calculus Final Review Test 1 (Unit 13-14)

• d/dx (sin^-1(x))

  1/sqrt(1-x^2)
• Chain Rule

  f'(g(x))g'(x)
• Steps on doing Implicit Differentiation

  1. Differentiate both sides
  2. Put terms with a f'(x)'s on one side of the equation and terms without an f'(x) on the other side
  3. Factor out f'(x)
  4. Solve for f'(x)
• d/dx (tan^-1(x))

  1/(1+x^2)
• d/dx secx

  secxtanx
• d/dx tanx

  sec^2x
• d/dx cotx

  -csc^2x
• d/dx cscx

  -cscx cotx
• y= log base a (x)

  a^y = x
• d/dx (log base a (x))

  1/ x ln(a)
• d/dx (ln(x))

  1/x
• log (mn)

  log m + log n
• log (m/n)

  log m - log n
• log (m^r)

  r log (m)
• With log functions, absolute values...

  don't matter when you take the derivative:

  y = ln | f(x) |y' = 1/f(x) * f'(x)
• Quotient Rule

  f'(x)g(x) - g'(x)f(x) / g(x)^2
• Product Rule

  f'(x)g(x) + g'(x)f(x)
• Logarithmic Function

  f(x)=log(x)