Derivatives of Trigonometric Functions (+ Inverses!)

now updated to have inverses as well

ƒ(x) = sin(x)

ƒ’(x) = cos(x)

ƒ(x) = cos(x)

ƒ’(x) = -sin(x)

ƒ(x) = tan(x)

ƒ’(x) = sec²(x)

ƒ(x) = cot(x)

ƒ’(x) = -csc²(x)

ƒ(x) = sec(x)

ƒ’(x) = sec(x) × tan(x)

ƒ(x) = csc(x)

ƒ’(x) = -csc(x) × cot(x)

ƒ(x) = sin⁻¹(x); ƒ(x) = arcsin(x)

ƒ’(x) = 1/√(1-x²)

ƒ(x) = cos⁻¹(x); ƒ(x) = arccos(x)

ƒ’(x) = -1/√(1-x²)

ƒ(x) = tan⁻¹(x); ƒ(x) = arctan(x)

ƒ’(x) = 1/(1+x²)

ƒ(x) = cot⁻¹(x); ƒ(x) = arccot(x)

ƒ’(x) = -1/(1+x²)

ƒ(x) = sec⁻¹(x); ƒ(x) = arcsec(x)

ƒ’(x) = 1/(|x|√(x²-1))

ƒ(x) = csc⁻¹(x); ƒ(x) = arccsc(x)

ƒ’(x) = -1/(|x|√(x²-1))