derivatives of exponential functions

y'=loga*g(x): log base of a constant times a function

1/ln(a) * g'(x)/g(x): one over the natural log of the constant times the derivative of the function over the function

y'=loga*x: log base of a constant times x

1/ln(a)*x: one over the natural log of the base times x

y'=ln(x): the natural log of x

1/x: one over x

y'= e^g(x): e raised to a function

e^g(x)*g'(x): e raised to a function multiplied by the derivative of the function

y'=e^x: e to the x

e^x: e to the x

y'=lng(x): the natural log of a function

g'(x)/g(x): the derivative of the function/the function

y'=a^g(x): constant raised to a function

ln(a)*a^g(x)*g'(x): natural log of the constant times the constant raised to a function times the derivative of the function

y'=a^x: constant raised to the x

ln(a)*a^x: natural log of the constant multiplied by the constant raised to the x