Constant:  If y = k, any constant, then dy/dx = 0

Example:    If f(x)=7, then f '(x)=0

Power Rule:  If y=uⁿ,  then dy/dx = n u^n-1du/dx

Example:    If g(t)= (t² + t - 5)⁷, then g '(t)= 7(t²+t-5)⁶ (2t+1)

General Expo: If y = a^u, then dy/dx = a^u (ln a) du/dx

Example:  If y=2^x2, then y'=2^x2(ln2)(2x)

The special Expo: If y = e^u, then dy/dx = e^u du/dx

Example:  If  C=e^(1-2t), then C ' = e^(1-2t)(-2)

The natural log: If y = ln(u), then dy/dx = (1/u) du/dx 

Example:  If P(x)= ln(x²-4x+33), then P '(x)= [1/(x²-4x+33)] (2x-4)

The trig fcns:     If y = sin(u), then dy/dx = cos(u) du/dx

                        If y = cos(u), then dy/dx = - sin(u) du/dx

                        If y = tan(u), then dy/dx = sec²(u) du/dx

                        If y = sec(u), then dy/dx = sec(u)tan(u) du/dx

                        If y = csc(u), then dy/dx = - csc(u)cot(u) du/dx

                        If y = cot(u), then dy/dx = - csc²(u) du/dx

The inverse trig fcns:

                        If y = sin^-1(u), then dy/dx =  du/dx / √(1-u²)

                        If y = cos^-1(u), then dy/dx = - du/dx / √(1-u²)

                        If y = tan^-1(u), then dy/dx = du/dx / (1+u²)

                        If y = sec^-1(u), then dy/dx = du/dx / |u| √(u²-1), |u|>1

                        If y = csc^-1(u), then dy/dx = - du/dx / |u| √(u²-1), |u|>1

                        If y = cot^-1(u), then dy/dx = - du/dx / (1+u²)

Sums:   If y = u + v,  then dy/dx = du/dx + dv/dx

Product Rule:  If y = uv, then dy/dx = u dv/dx + v du/dx

Quotient Rule:  If y = u/v, then dy/dx = [v du/dx - u dv/dx] / v²

Implicit differentiation
    (take the derivative of both sides then solve for the desired derivative)

Logarithmic  differentiation
    (take the natural log of both sides and simplify then differentiate implicitly and solve for the desired derivative)

General log fcn: If y=log_au, then dy/dx = [1/(ulna)]du/dx