diferensial rumus lengkap

Power of x.

c = 0 x = 1 xn = n x(n-1)
Proof

Exponential / Logarithmic

ex = ex
Proof
bx = bx ln(b)
Proof
ln(x) = 1/x
Proof

Trigonometric

sin x = cos x
Proof
csc x = -csc x cot x
Proof
cos x = – sin x
Proof
sec x = sec x tan x
Proof
tan x = sec2 x
Proof
cot x = – csc2 x
Proof

Inverse Trigonometric

arcsin x  = 


sqrt(1 – x2)

arccsc x =  -1


|x| sqrt(x2 – 1)

arccos x =   -1 


sqrt(1 – x2)

arcsec x =  1


|x| sqrt(x2 – 1)

arctan x = 


1 + x2

arccot x =  -1


1 + x2

Hyperbolic

sinh x = cosh x
Proof
csch x = – coth x csch x
Proof
cosh x = sinh x
Proof
sech x = – tanh x sech x
Proof
tanh x = 1 – tanh2 x
Proof
coth  x = 1 – coth2 x
Proof

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