public void TestMultiplicationByConstant()
{
Symbol y = new Symbol("y");
Symbol x = new Symbol("x");
var expr = y <= 4 * x;
var ddx = new DerivativeSymbol(y) <= 4;
Assert.AreEqual(ddx, expr.Differentiate(x).Simplify());
}
public void TestChainRule()
{
Symbol y = new Symbol("y");
Symbol x = new Symbol("x");
var expr = y <= Trig.Sin(x);
var dx = new DerivativeSymbol(y) <= Trig.Cos(x) * 1;
Assert.AreEqual(dx, expr.Differentiate(x).Simplify());
}
public void TestDifferenceRule()
{
Symbol y = new Symbol("y");
Symbol x = new Symbol("x");
var expr = y <= x - 5;
var ddx = new DerivativeSymbol(y) <= 1;
Assert.AreEqual(ddx, expr.Differentiate(x).Simplify());
}
public void TestPowerRule()
{
Symbol y = new Symbol("y");
Symbol x = new Symbol("x");
var expr = y <= (x ^ 2);
var ddx = new DerivativeSymbol(y) <= 2 * (x ^ 1);
Assert.AreEqual(ddx, expr.Differentiate(x).Simplify());
}
public void TestQuotientRule()
{
Symbol z = new Symbol("z");
Symbol y = new Symbol("y");
Symbol x = new Symbol("x");
var expr = y <= x / z;
var ddx = new DerivativeSymbol(y) <= (1 * z - new DerivativeSymbol(z) * x) / (z * z);
Assert.AreEqual(ddx, expr.Differentiate(x).Simplify());
}
public void TestProductRule()
{
Symbol z = new Symbol("z");
Symbol y = new Symbol("y");
Symbol x = new Symbol("x");
var expr = y <= x * z;
var ddx = new DerivativeSymbol(y) <= 1 * z + x * new DerivativeSymbol(z);
Assert.AreEqual(ddx, expr.Differentiate(x).Simplify());
}
public override bool Equals(object obj)
{
return(obj switch {
DerivativeSymbol expr => expr.baseSymbol.Equals(this.baseSymbol),
_ => base.Equals(obj)
});
