abs(x + du) ~= x + du or -(x + du)
acos(a + du) ~= acos(a) - 1 / sqrt(1 - a**2) du
asin(a + du) ~= asin(a) - 1 / sqrt(1 - a**2) du
atan(a + du) ~= atan(a) + 1 / (1 + a**2) du
Defined with "this" as the y coordinate: this.
Defined with "this" as the y coordinate: this.atan2(a) == atan2(this, a) == atan(this / a) atan2(b + dv, a + du) ~= atan2(b, a) + (- b du + a dv) / (a2 + b2)
cos(a + du) ~= cos(a) - sin(a) du
cosh(a + du) ~= cosh(a) + sinh(a) du
exp(a + du) ~= exp(a) + exp(a) du
log(a + du) ~= log(a) + du / a
pow -- both base (this) and exponent are differentiable functions.
pow -- both base (this) and exponent are differentiable functions. (a + du)(b + dv) ~= ab + b * a(b-1) du + ab log(a) dv
pow -- base (this) is a differentiable function, exponent is a constant.
pow -- base (this) is a differentiable function, exponent is a constant. pow(a + du, p) ~= pow(a, p) + p * pow(a, p-1) du
This is consistent with abs
sin(a + du) ~= sin(a) + cos(a) du
sinh(a + du) ~= sinh(a) + cosh(a) du
sqrt(a + du) ~= sqrt(a) + du / (2 sqrt(a))
tan(a + du) ~= tan(a) + (1 + tan(a)**2) du
tanh(a + du) ~= tanh(a) + (1 - tanh(a)**2) du