Table of derivatives of trigonometric functions and inverse trigonometric functions

1. (sin x )' = cos x 
   The derivative of the sine of x is equal to the cosine of x
2. (cos x )' = -sin x 
   The derivative of the cosine of x is equal to minus the sine of x
3. (tg x)' = 1/ cos²x = 1 + tg² x 
   The derivative of the tangent of x can be found as 
   
   • one divided by cosine squared x
   • one plus tangent squared x
4. (ctg x)' = - 1/ sin²x = -(1 + ctg² x) 
   The derivative of the cotangent of x can be similarly represented by two expressions: 
   
   • minus one divided by sine square x
   • minus the sum of one and the cotangent squared x
5. (arcsin x)' = 1/(√(1-x²))
   The derivative of the arcsine of x is equal to one divided by the root of the difference of one and x squared
6. (arccos x)' = -1/(√(1-x²))
   The derivative of the arc cosine x is equal to minus one divided by the root of the difference of one and x squared
7. ( arctg x )' = 1 / ( 1 + x² ) 
   The derivative of the arc tangent of x is equal to a fraction whose numerator is one, and the denominator is one plus x squared
8. ( arcctg x )' = -1 / ( 1 + x² ) 
   The derivative of the arc tangent of x is minus one divided by the sum of one and x squared
9. (sex x)' = tg x sec x
   The derivative of the secant of x is equal to the product of the tangent of x and the secant of x
10. (cosec x)' = -ctg x cosec x
    The derivative of the cosecant of x is minus the cotangent of x times the cosecant of x
11. (arcsec x)' = 1 / (|x|√(x² -1))
    The derivative of the arcsecant x is equal to a fraction, in the numerator of which there is one, and in the denominator the product of the module x and the square root of the difference x squared and one
12. (arccosec x)' = - 1 / (|x|√(x² -1)) 
    The derivative of the arccosecant x is equal to a fraction, in the numerator of which is minus one, and in the denominator the product of the modulus x and the root of the square difference x square and one