Basic Differentiation Rules (Stated)
The derivative of base a is..
The derivative of a base a is (ln a)a^u⋅u' (Exponential Base Rule)
The derivative of a constant is...
The derivative of a constant is zero. (Constant Rule)
The derivative of a u multiplied by a constant is...
The derivative of a constant multiple, k⋅u is k⋅u' (Constant Multiple Rule)
The derivative of e^u is...
The derivative of a e^u is e^u⋅u' (Exponential Rule)
The derivative of the sum or difference of u and v is...
The derivative of a sum and difference of u ± v is u' ± v' (Sum and Difference Rule)
The derivative of Arc-Cosine is...
The derivative of arc-cosine of u is -u'/√(1-u²) (Arc-Cosine Rule)
The derivative of Arc-Cotangent is...
The derivative of arc-cotangent of u is -u'/(u²+1) (Arc-Cotangent Rule)
The derivative of Arc-Cosecant is...
The derivative of arc-secant of u is -u'/[abs u⋅√(u²-1)] (Arc-Cosecant Rule)
The derivative of Arc-Secant is...
The derivative of arc-secant of u is u'/[abs u⋅√(u²-1)] (Arc-Secant Rule)
The derivative of Arc-Sine is...
The derivative of arc-sine of u is u'/√(1-u²) (Arc-Sine Rule)
The derivative of Arc-Tangent is...
The derivative of arc-tangent of u is u'/(u²+1) (Arc-Tangent Rule)
The derivative of log base a of u is...
The derivative of log base a of u is u'/[(ln a)⋅u] (Log Base a Rule)
The derivative of the absolute value of u is...
The derivative of the absolute value of u is [u/(abs u)]⋅u' where u ≠ 0. (Absolute Value Rule)
The derivative of Cosecant is...
The derivative of the cosecant of u is -(csc u⋅cot u)u' (Cosecant Rule)
The derivative of Cosine is...
The derivative of the cosine of u is -(sin u)u' (Cosine Rule)
The derivative of Cotangent is...
The derivative of the cotangent of u is -(csc² u)u' (Cotangent Rule)
The derivative of the natural log of u is...
The derivative of the natural log of u is u'/u. (Natural Log Rule)
The derivative of Secant is...
The derivative of the secant of u is (sec u⋅tan u)u' (Secant Rule)
The derivative of Sine is...
The derivative of the sine of u is (cos u)u' (Sine Rule)
The derivative of Tangent is...
The derivative of the tangent of u is (sec² u)u' (Tangent Rule)
The derivative of u divided by v is...
The derivative of u multiplied by v is (vu' - uv')/(v²) where v ≠ 0 (Quotient Rule)
The derivative of u to the n power is...
The derivative of uⁿ is n⋅uⁿ⁻¹⋅u' (General Power Rule)
The derivative of u multiplied by v is...
The derivative of u⋅v is uv' + vu' (Product Rule)
The derivative of x is...
The derivative of x is one. (Simple Power Rule)
The derivative of ƒ of u is...
The derivative of ƒ(u) is ƒ'(u)⋅u' (Chain Rule)
