Derivative Rules

Constant Rule: d/dx [c] = ?

0

Constant Multiple Rule: d/dx [c·f(x)] = ?

c·f′(x)

Sum Rule: d/dx [f(x) + g(x)] = ?

f′(x) + g′(x)

Difference Rule: d/dx [f(x) − g(x)] = ?

f′(x) − g′(x)

Product Rule: d/dx [f(x)·g(x)] = ?

f′(x)g(x) + f(x)g′(x)

Quotient Rule: d/dx [f(x) / g(x)] = ?

[g(x)f′(x) − f(x)g′(x)] / [g(x)]²

Chain Rule: d/dx [f(g(x))] = ?

f′(g(x))·g′(x)

Power (Basic): d/dx [xⁿ] = ?

n·xⁿ⁻¹

Power (Chain): d/dx [uⁿ] = ?

n·uⁿ⁻¹·u′

Sine (Basic): d/dx [sin x] = ?

cos x

Sine (Chain): d/dx [sin u] = ?

cos(u)·u′

Cosine (Basic): d/dx [cos x] = ?

−sin x

Cosine (Chain): d/dx [cos u] = ?

−sin(u)·u′

Tangent (Basic): d/dx [tan x] = ?

sec²x

Tangent (Chain): d/dx [tan u] = ?

sec²(u)·u′

Cosecant (Basic): d/dx [csc x] = ?

−csc x·cot x

Cosecant (Chain): d/dx [csc u] = ?

−csc(u)cot(u)·u′

Secant (Basic): d/dx [sec x] = ?

sec x·tan x

Secant (Chain): d/dx [sec u] = ?

sec(u)tan(u)·u′

Cotangent (Basic): d/dx [cot x] = ?

−csc²x

Cotangent (Chain): d/dx [cot u] = ?

−csc²(u)·u′

Exponential base e (Basic): d/dx [eˣ] = ?

eˣ

Exponential base e (Chain): d/dx [eᵘ] = ?

eᵘ·u′

Exponential base a (Basic): d/dx [aˣ] = ?

aˣ·ln(a)

Exponential base a (Chain): d/dx [aᵘ] = ?

aᵘ·ln(a)·u′

Natural Log (Basic): d/dx [ln x] = ?

1/x

Natural Log (Chain): d/dx [ln u] = ?

(1/u)·u′ or u′/u

Log base a (Basic): d/dx [logₐ x] = ?

1/(x·ln a)

Log base a (Chain): d/dx [logₐ u] = ?

u′/(u·ln a)