Table of Derivatives

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Table of Derivatives

(Math | Calculus | Derivatives | Table Of)

Power of x.

c = 0 x = 1 xⁿ = n x^(n-1)
Proof

Exponential / Logarithmic

e^x = e^x
Proof b^x = b^x 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 = 1
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
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

Those with hyperlinks have proofs.