Derivatives

always be negative

Derivatives of functions with "co" in their name will...

just be each other

Derivatives of cos and sin will....

always be squared, and either secant or cosecant

Derivatives of tangent and cotangent will...

just be themselves multiplied by either tan or cotangent

Derivatives of secant and cosecant will...

-sin x

d/dx [cos x]

cos x

d/dx [sin x]

sec^2 x

d/dx [tan x]

-csc^2 x

d/dx [cot x]

-csc x cot x

d/dx [csc x]

sec x tan x

d/dx [sec x]

u' / 1+u^2

d/dx [arctan u]

-u'/√(1-u^2)

d/dx [arccos u]

u'/√(1-u^2)

d/dx [arcsin u]

e^x

d/dx [e^x]

(e^u) (u')

d/dx [e^u]

1/x

d/dx [ln x]

(1/u)(u')

d/dx [ln u]

(ln a)(a^u)(u')

d/dx [a^u]

u'v + uv'

The product Rule: d/dx [uv] =

(vu'-uv') / v^2

The Quotient Rule: d/dx [u/v] =

nu^(n-1) u'

Chain rule (Exponents) d/dx [u^n]

f'(u)u'

Chain Rule (Trigonometry) d/dx [f(u)]

1st and 2d quadrants, 0/2π - π

Range of arccos

4th and 1st quadrant, 3π/2 - π/2

Range of arcsin & arctan

1 / f' ( g(x) )

If f and g are inverses of each other, then g'(x) =

x

e^ln x

x

ln e^x