Common Derivative Formulas

y = c

y’ = 0

y = xⁿ

y’ = nx^n-1

y = √x

y’ = 1 / (2√x)

y = 1 / x

y’ = -1 / x²

y = e^x

y’ = e^x

y = a^x

y’ = a^xln(a)

y = ln(x)

y’ =1 / x

y = log_a(x)

y’ = 1 / xln(a)

y = sin(x)

y’ = cos(x)

y = cos(x)

y’ = -sin(x)

y = tan(x)

y’ = sec²(x)

y = cot(x)

y’ = -csc²(x)

y = sec(x)

y’ = sec(x)tan(x)

y = csc(x)

y’ = -csc(x)cot(x)

y = sin^-1

y’ = 1 / √(1 - x²)

y = cos^-1

y’ = -1 / √(1 - x²)

y = tan^-1

y’ = 1 / (1 + x²)

y = csc^-1

y’ = -1 / (lxl √(x² - 1))

y = sec^-1

y’ = 1 / (lxl √(x² - 1))

y = cot^-1

y’ = -1 / (1 + x²)