Derivatives of Trigonometric Functions
www.ocf.berkeley.edu › ~reinholz › edKnowledge of the derivatives of sine and cosine allows us to find the derivatives of all other trigono-metric functions using the quotient rule. Recall the following identities: tan(x) = sin(x) cos(x) cot(x) = cos(x) sin(x) sec(x) = 1 cos(x) csc(x) = 1 sin(x) Example 2 Find the derivatives of tan(x), cot(x), csc(x), and sec(x).
CALCULUS TRIGONOMETRIC DERIVATIVES AND INTEGRALS
www.csusm.edu › stemsc › handoutsCALCULUS TRIGONOMETRIC DERIVATIVES AND INTEGRALS TRIGONOMETRIC DERIVATIVES d dx (sin( x)) = cos( )·0 d dx (cos( )) = sin(0 d dx (tan( x)) = sec2( )· 0 d dx (csc( x)) = csc( )cot( )·0 d dx (sec( )) = sec( )tan(0 d dx (cot(x)) = csc2( x)· 0 d dx (sin 01 (x)) =p 1 1x2 ·xd dx (cos (tan1(x)) = p 1 1x2 0 d dx 1 1 1+x2 ·x 0 d dx (csc 1(x)) = 1 x p x21 ·x0 d dx (sec (cot1 (x)) =1 x p x21 ·x0 d dx 1 1
Derivatives of Trigonometric Functions
www.personal.psu.edu › Notes-Derivatives_of_Trigex. Find the derivative of csc x. x x x x x dx d dx d x dx x d x dx d 2 sin2 sin 0 1cos (sin ) sin 1 1 sin sin 1 csc ⋅ − ⋅ = − = = x x x x x x x csc cot sin cos sin 1 sin cos 2 =− ⋅ =− − = Therefore, x x x dx d csc =−csc cot The complete list of derivatives of trigonometric functions: 1. x x dx d sin =cos 2. x x dx d cos =−sin 3. x x dx d tan =sec2 4. x x x dx d sec =sec tan 5. x x dx