protected override Number Evaluate(Number number)
{
return(NumberMath.Ln(number));
}
public override IExpression?Differentiate(string byVariable)
{
if (Right is ConstantExpression)
{
// f(x) = g(x)^n
// f'(x) = n * g'(x) * g(x)^(n-1)
return
(new MultiplyExpression(new MultiplyExpression(Right, Left?.Differentiate(byVariable)),
new ExponentExpression(Left, new SubtractExpression(Right, new ConstantExpression(1)))));
}
var simple = Left?.Simplify();
if (simple is ConstantExpression constant)
{
// f(x) = a^g(x)
// f'(x) = (ln a) * g'(x) * a^g(x)
var a = constant.Value;
return(new MultiplyExpression(new MultiplyExpression(new ConstantExpression(NumberMath.Ln(a)), Right?.Differentiate(byVariable)), new ExponentExpression(simple, Right)));
}
throw new CannotDifferentiateException(Resources.CanotDifferentiate);
}