Trigonometric Functions Derivatives is basically differentiation of Trigonometric Functions to find the rate at which function changes with respect to a variable. Six trigonometric functions that we are going to differentiate are sin (X), cos (X), tan (X), cosec (X), sec (X) and cot (X). One should have good knowledge of various Differentiation Rules to find Derivatives of Trigonometric Functions.
Basic derivatives are considered to be of sin (X) and cos(X). If these are known to one, others can easily be evaluated using trigonometric formulae because rest can be represented in terms of sine and cosine. Different rules of differentiation related to constants, exponents, fractions etc. are important to imitate the calculation for derivatives of trigonometric functions. Here, are some general formulae which can be used in complex situations involving trigonometric functions.
D (sin X) / DX = cos X,
D (cos X) / DX = - sin X,
D (tan X) / DX = D (sin X / cos X) / DX,
Using rules for differentiating a fraction in above situation:
= (cos2 X + sin2 X) / cos2 X = 1 / cos2 X = sec2 X,
D (cot X) / DX = D (cos X / sin X) / DX = (- cos2 X - sin2 X) / sin2 X = - (1 + cot2 X) = - cosec2 X,
D (sec X) / DX = D (1 / cos X) / DX = (sinX / cos2 X) = (1 / cos X) * (sin X / cos X) = sec X tan X,
D (cosec X) / DX = D (1 / sin X) / DX = - (cosX / sin2 X) = - (1 / sin X) * (cos X / sin X) = - cosec X cot X.