Derivative of Trigonometric and Hyperbolic Functions and their Inverses

Derivative of Trigonometric Functions

d(sinx)/dx = cosx

d(cosx)/dx = –sinx

d(tanx)/dx = sec sq. x

d(cotx)/dx = –cosec sq. x

d(secx)/dx = secx.tanx

d(cosecx)/dx = –cosecx.cotx

Derivative of Hyperbolic Functions

d(sinhx)/dx = coshx

d(coshx)/dx = sinhx

d(tanhx)/dx = sech sq. x

d(cothx)/dx = –cosecsq. x

d(sechx)/dx = –sechx.tanhx

d(cosechx)/dx = –cosechx.cothx

 

Derivative of Inverse Trigonometric Functions

d(sin^-1x)/dx = 1 / √ (1-x sq. )

d(cos^-1x)/dx = -1 / √ (1-x sq. )

d(tan^-1x)/dx = 1 / (1+x sq. )

d(cot^-1x)/dx = -1 / (1+x sq. )

d(sec^-1x)/dx = 1 / [x√(x sq. -1)]

d(cosec^-1x)/dx = -1 / [x√(x sq. -1)]

 

Derivative of Inverse Hyperbolic Functions

d(sinh^-1x)/dx = 1 / √(1+x sq. )

d(cosh^-1x)/dx = 1 / √(x sq. -1)

d(tanh^-1x)/dx = 1 / (1-x sq. )

d(coth^-1x)/dx = -1 / (x sq. -1) = 1 / (1-x sq. )

d(sech^-1x)/dx = -1 / [x√(1-x sq. )]

d(cosech^-1x)/dx = -1 / [x√(x sq. +1)]

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