d/dx [arcsin u]
u’ / sqrt(1-u²)
d/dx [arctan u]
u’ / 1 + u²
d/dx [arcsec u]
u’ / |u| sqrt(1-u²)
d/dx [arcsin (u/a)]
u’ / sqrt(a² - u²)
d/dx [arctan (u/a)]
(a)(u’ ) / a² + u²
d/dx [tan x]
sec² x
d/dx [cot x]
-csc² x
d/dx [sec x]
sec x tan x
csc x
-csc x cot x
d/dx [x² + y² ]
2x + 2y (dy/dx)
d/dx [ xy ]
(1)(y) + (dy/dx) (x)
d/dx [ x² * ln x ]
(2x)(ln x) + (1/x)(x²)
d/dx [ e^x sec x ]
(e^x)(sec x) + (sec x tan x) (e^x)
d/dx [ 3^sqrt(x-2) ]
( (3^sqrt(x-2)) (ln 3) ) (1/(2)(sqrt(x-2)) )
d/dx [ cos^4 (6x) ]
(4(cos³(6x)) (-sin (6x) (6))
d/dx [ f(x) + g(x) ]
f’(x) + g’(x)
d/dx [ f(x) g(x) ]
(f’(x))(g(x)) + (g’(x)) (f(x))
d/dx [ f(x)/g(x) ]
( (f’(x))(g(x)) - (g’(x))(f(x)) ) / g(x)²
d/dx [ f(g(x)) ]
f’(g(x)) (g’(x))
d/dx [ sqrt(x) ]
1 / 2 sqrt(x)