public void DerivativeTest3()
{
// x ^ 3
Variable x = new Variable("x");
Number num1 = new Number(3);
IExpression exp = new Pow(x, num1);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("1 * (3 * (x ^ (3 - 1)))", deriv.ToString());
num1.Value = 4;
Assert.AreEqual("x ^ 4", exp.ToString());
Assert.AreEqual("1 * (3 * (x ^ (3 - 1)))", deriv.ToString());
// 2 ^ (3x)
Number num2 = new Number(2);
num1 = new Number(3);
Mul mul = new Mul(num1, x.Clone());
exp = new Pow(num2, mul);
deriv = exp.Differentiate();
Assert.AreEqual("(ln(2) * (2 ^ (3 * x))) * (3 * 1)", deriv.ToString());
num1.Value = 4;
Assert.AreEqual("2 ^ (4 * x)", exp.ToString());
Assert.AreEqual("(ln(2) * (2 ^ (3 * x))) * (3 * 1)", deriv.ToString());
}
public void AddDiffNum_VarSubNum_()
{
// 2 + (x - 2)
var add = new Add(new Number(2), new Sub(new Variable("x"), new Number(2)));
var expected = new Variable("x");
SimpleTest(add, expected);
}
public DefiniteIntegral(
IExpression expression,
Variable variable,
IExpression left,
IExpression right)
: base(new[] { expression, variable, left, right }, 4)
{
}
public void AbsDerivativeTest2()
{
var num = new Number(2);
var x = new Variable("x");
var mul = new Mul(num, x);
var exp = new Abs(mul);
var deriv = Differentiate(exp);
Assert.Equal("2 * 1 * ((2 * x) / abs(2 * x))", deriv.ToString());
num.Value = 3;
Assert.Equal("abs(3 * x)", exp.ToString());
Assert.Equal("2 * 1 * ((2 * x) / abs(2 * x))", deriv.ToString());
}
public void DerivativeTest2()
{
// log(x, 2)
Number num = new Number(2);
Variable x = new Variable("x");
IExpression exp = new Log(x, num);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("1 / (x * ln(2))", deriv.ToString());
num.Value = 4;
Assert.AreEqual("log(4, x)", exp.ToString());
Assert.AreEqual("1 / (x * ln(2))", deriv.ToString());
}
public void AbsDerivativeTest2()
{
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Abs(mul);
IExpression deriv = Differentiate(exp);
Assert.AreEqual("(2 * 1) * ((2 * x) / abs(2 * x))", deriv.ToString());
num.Value = 3;
Assert.AreEqual("abs(3 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) * ((2 * x) / abs(2 * x))", deriv.ToString());
}
public void DerivativeTest3()
{
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Tan(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(2 * 1) / (cos(2 * x) ^ 2)", deriv.ToString());
num.Value = 5;
Assert.AreEqual("tan(5 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) / (cos(2 * x) ^ 2)", deriv.ToString());
}
public void DerivativeTest2()
{
// lg(2x)
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Lg(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(2 * 1) / ((2 * x) * ln(10))", deriv.ToString());
num.Value = 3;
Assert.AreEqual("lg(3 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) / ((2 * x) * ln(10))", deriv.ToString());
}
public void DerivativeTest3()
{
// cot(2x)
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Cot(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("-((2 * 1) / (sin(2 * x) ^ 2))", deriv.ToString());
num.Value = 3;
Assert.AreEqual("cot(3 * x)", exp.ToString());
Assert.AreEqual("-((2 * 1) / (sin(2 * x) ^ 2))", deriv.ToString());
}
public void DerivativeTest2()
{
// arcsec(2x)
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Arcsec(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(2 * 1) / (abs(2 * x) * sqrt(((2 * x) ^ 2) - 1))", deriv.ToString());
num.Value = 4;
Assert.AreEqual("arcsec(4 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) / (abs(2 * x) * sqrt(((2 * x) ^ 2) - 1))", deriv.ToString());
}
public void DerivativeTest3()
{
// exp(2x)
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Exp(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(2 * 1) * exp(2 * x)", deriv.ToString());
num.Value = 6;
Assert.AreEqual("exp(6 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) * exp(2 * x)", deriv.ToString());
}
public void DerivativeTest3()
{
// arccos(2x)
Number num = new Number(2);
Variable x = new Variable("x");
Mul mul = new Mul(num, x);
IExpression exp = new Arccos(mul);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
num.Value = 6;
Assert.AreEqual("arccos(6 * x)", exp.ToString());
Assert.AreEqual("-((2 * 1) / sqrt(1 - ((2 * x) ^ 2)))", deriv.ToString());
}
public void DerivativeTest2()
{
Number num1 = new Number(2);
Variable x = new Variable("x");
Mul mul1 = new Mul(num1, x);
Number num2 = new Number(3);
Mul mul2 = new Mul(num2, x.Clone());
IExpression exp = new Sub(mul1, mul2);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(2 * 1) - (3 * 1)", deriv.ToString());
num1.Value = 5;
num2.Value = 4;
Assert.AreEqual("(5 * x) - (4 * x)", exp.ToString());
Assert.AreEqual("(2 * 1) - (3 * 1)", deriv.ToString());
}
public void DerivativeTest3()
{
// (2x) / (3x)
Number num1 = new Number(2);
Variable x = new Variable("x");
Mul mul1 = new Mul(num1, x);
Number num2 = new Number(3);
Mul mul2 = new Mul(num2, x.Clone());
IExpression exp = new Div(mul1, mul2);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("(((2 * 1) * (3 * x)) - ((2 * x) * (3 * 1))) / ((3 * x) ^ 2)", deriv.ToString());
num1.Value = 4;
num2.Value = 5;
Assert.AreEqual("(4 * x) / (5 * x)", exp.ToString());
Assert.AreEqual("(((2 * 1) * (3 * x)) - ((2 * x) * (3 * 1))) / ((3 * x) ^ 2)", deriv.ToString());
}
public void MulSecondOne()
{
var mul = new Mul(new Variable("x"), new Number(1));
var expected = new Variable("x");
SimpleTest(mul, expected);
}
public void PowerOne()
{
var pow = new Pow(new Variable("x"), new Number(1));
var expected = new Variable("x");
SimpleTest(pow, expected);
}
public void MulSameVar8()
{
// 2x * 3x
var var = new Variable("x");
var mul = new Mul(new Mul(new Number(2), var), new Mul(new Number(3), var));
var expected = new Mul(new Number(6), new Pow(var, new Number(2)));
SimpleTest(mul, expected);
}
public void MulSameVar9()
{
// (x * 2) * (x * 3)
var var = new Variable("x");
var mul = new Mul(new Mul(var, new Number(2)), new Mul(var, new Number(3)));
var expected = new Mul(new Number(6), new Pow(var, new Number(2)));
SimpleTest(mul, expected);
}
public void RootOne()
{
var root = new Root(new Variable("x"), new Number(1));
var expected = new Variable("x");
SimpleTest(root, expected);
}
public void MulSameVar11()
{
// 2x * -3x
var var = new Variable("x");
var mul = new Mul(new Mul(new Number(2), var), new Mul(new Number(-0.5), var));
var expected = new UnaryMinus(new Pow(var, new Number(2)));
SimpleTest(mul, expected);
}
public void MulSameVar1()
{
// x * x
var var = new Variable("x");
var mul = new Mul(var, var);
var expected = new Pow(var, new Number(2));
SimpleTest(mul, expected);
}
public void MulNegativeRightParamTest1()
{
// sin(cos(x))
var x = new Variable("x");
var mul = new Mul(new Cos(new Cos(x)), new UnaryMinus(new Sin(x)));
var expected = new UnaryMinus(new Mul(new Sin(x), new Cos(new Cos(x))));
SimpleTest(mul, expected);
}
public void MulDiff_VarDivNum_MulNum()
{
// (x / 2) * 2
var mul = new Mul(new Div(new Variable("x"), new Number(2)), new Number(2));
var expected = new Variable("x");
SimpleTest(mul, expected);
}
public void SinhArsinh()
{
var exp = new Sinh(new Arsinh(new Variable("x")));
var expected = new Variable("x");
SimpleTest(exp, expected);
}
public void DoubleUnary()
{
var un = new UnaryMinus(new UnaryMinus(new Variable("x")));
var expected = new Variable("x");
SimpleTest(un, expected);
}
public void SecArcsec()
{
var exp = new Sec(new Arcsec(new Variable("x")));
var expected = new Variable("x");
SimpleTest(exp, expected);
}
public void DivSameVars()
{
var x = new Variable("x");
var div = new Div(x, x);
var expected = new Number(1);
SimpleTest(div, expected);
}
/// <summary>
/// Initializes a new instance of the <see cref="Derivative"/> class.
/// </summary>
/// <param name="expression">The expression.</param>
/// <param name="variable">The variable.</param>
public Derivative(IExpression expression, Variable variable)
: base(new[] { expression, variable }, 2)
{
}
public void MulDiffNumMul_VarDivNum_()
{
// 2 * (x / 2)
var mul = new Mul(new Number(2), new Div(new Variable("x"), new Number(2)));
var expected = new Variable("x");
SimpleTest(mul, expected);
}
public void DerivativeTest2()
{
// 2x
Number num = new Number(2);
Variable x = new Variable("x");
IExpression exp = new Mul(num, x);
IExpression deriv = exp.Differentiate();
Assert.AreEqual("2 * 1", deriv.ToString());
num.Value = 3;
Assert.AreEqual("3 * x", exp.ToString());
Assert.AreEqual("2 * 1", deriv.ToString());
}