derivatives

d/dx [c]

0 (c = constant)

d/dx [x^n]

n*x^(n-1)

d/dx [c*f(x)]

c*f'(x)

d/dx [f(x) ± g(x)]

f'(x) ± g'(x)

d/dx [e^x]

e^x

d/dx [e^u]

e^u * u' (Chain Rule)

d/dx [a^x]

a^x * ln(a) (a > 0, a≠1)

d/dx [ln x]

1/x (x > 0)

d/dx [ln u]

u'/u (Chain Rule)

d/dx [logₐ x]

1/(x ln a) (a > 0, a≠1)

d/dx [sin x]

cos x

d/dx [cos x]

sec² x

d/dx [cot x]

-csc² x

d/dx [sec x]

sec x tan x

d/dx [csc x]

-csc x cot x

d/dx [sin⁻¹ x]

1/√(1-x²)

d/dx [cos⁻¹ x]

-1/√(1-x²)

d/dx [tan⁻¹ x]

1/(1+x²)

d/dx [cot⁻¹ x]

-1/(1+x²)

d/dx [sec⁻¹ x]

1/(|x|√(x²-1))

d/dx [csc⁻¹ x]

-1/(|x|√(x²-1))

d/dx [f(x)*g(x)]

f'(x)g(x) + f(x)g'(x)

d/dx [f(x)/g(x)]

[f'(x)g(x) - f(x)g'(x)] / [g(x)]²

d/dx [f(g(x))]

f'(g(x)) * g'(x)

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