Derivatives and Anti-derivatives

d/dx [sin x]

cos x

d/dx [cos x]

-sin x

d/dx [tan x]

sec^2 x

d/dx [sec x]

sec x tan x

d/dx [cot x]

-csc^2 x

d/dx [csc x]

-csc x cot x

anti-derivative of cos x dx

sin x + C

anti-derivative of sin x dx

-cos x + C

anti-derivative of sec^2 x dx

tan x + C

anti-derivative of sec x tan x dx

sec x + C

anti-derivative of csc^2 x dx

-cot x + C

anti-derivative of csc x cot x dx

-csc x + C

d/dx [e^kx]

(1/k) e^kx

anti-derivative (1/k) e^kx

e^kx

d/dx [arcsin(x/a)]

1 / √(a²-x²)

anti-derivative of 1 / √(a²-x²)

(1/k)arcsin(kx)

d/dx [arctan(x/a)]

[1/(a²+x²)]

anti-derivative of [1/(a²+x²)]

(1/k) arctan(kx)

d/dx [arcsec(x/a]

1/(x√(x²-a²))

anti-derivative of 1/(x√(x²-a²))

(1/k) arcsec(x/a)

d/dx (sinhx)

cosh(x)

d/dx (coshx)

sinh(x)

d/dx (tanh(x))

sech²(x)

d/dx (csch(x))

-csch(x)coth(x)

d/dx (sech(x))

-sech(x)tanh(x)

d/dx coth(x)

-csch²(x)

d/dx sinh^-1(x/a)

1 / (√a²+x²)

d/dx cosh^-1(x/a)

1/(√x²-a²)

d/dx (tanh^-1(x/a))

1/(a²-x²)

d/dx csch^-1(x)

-1 / (|x|√x²+1)

d/dx sech^-1(x)

-1 / (x√1-x²)

d/dx coth^-1(x)

1/(1-x²)