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Trig function

d/dx sinx = cosx ;

d/dx cosx = -sinx ;

d/dx tanx = sec²x ;

d/dx cotx = -csc²x ;

d/dx secx = secx*tanx ;

d/dx cscx = -cscx*cotx ;

inverse trig

d/dx arcsin x = 1/√(1-x²);

d/dx arccos x = -1/√(1-x²);

d/dx arctan x = 1/(1+x²);

d/dx arccot x =-1/(1+x²);

d/dx arcsec x = 1/|x|*√(x² - 1);

d/dx arccsc x =-1/|x|*√(x² - 1);

exponential / logarithm function

d/dx(a^x) = a^x * ln(a) ; 

d/dx (logₐ(x)) = 1/x*ln(a) ;

hyperbolic trig function 

d/dx sinh x = cosh x ;

d/dx cosh x = sinh x ;

d/dx tanh x = sech² x ; 

d/dx coth x = -csch² x ;

d/dx sech x = -sech x * tanh x ;

d/dx csch x = -csch x * coth x ;