New Problem - Polynomial Derivative

Created a new problem where the user has to find the numerical derivative of a simple polynomial function. Includes edge case when the exponent is zero.

Author: Selbl

Problems/Polynomial Derivatives/learn.md

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+## Derivative of a Polynomial
+
+A function's derivative is a way of quantifying the function's slope at a given point. It allows us to understand whether the function is increasing, decreasing or flat at specific input. 
+
+Taking the derivative of a polynomial at a single point follows a straight-forward rule. This question will show the rule and the edge case you should be on the look-out for.
+
+### Mathematical Definition
+
+When calculating the slope of a function $f(x)$, we usually require two points $x_{1}$ and $x_{2}$ and use the following formula:
+
+$$
+\frac{f(x_{2}) - f(x_{1})}{x_{2} - x_{1}}
+$$
+
+A derivative generalizes that notion by calculating the slope of a function at a specific point.
+A derivative of a function $f(x)$ is mathematically defined as:
+
+$$
+\frac{d f(x)}{d x} = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
+$$
+
+Where:
+- $x$ is the input to the function
+- $h$ is the "step", which is equivalent to the difference $x_{2} - x_{1}$ in the two-point slope-formula
+
+Taking the limit as the step grows smaller and smaller, allow us to quantify the slope at a certain point, instead of having to consider two points as in other methods of finding the slope.
+
+When taking the derivative of a polynomial function $x^{n}$, where $n \neq 0$, then the derivative is: $n x^{n-1}$. In the special case where $n = 0$ then the derivative is zero. This is because $x^{0} = 1$ if $x \neq 0$.
+
+A positive derivative indicates that the function is increasing in that point, a negative derivative indicates that the function is decreasing at that point. A derivative equal to zero indicates that the function is flat, which could potentially indicate a function's minimum or maximum.

Problems/Polynomial Derivatives/solution.py

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+def polynomial_derivative(x: float,n: float) -> float:
+    if n == 0.0:
+        return 0.0
+    return round(n*(x**(n-1)),4)
+
+def test_polynomial_derivative():
+    # Test case 1
+    x,n = 10.0,0.0
+    expected_output = 0.0
+    assert polynomial_derivative(x,n) == expected_output, "Test case 1 failed"
+
+    # Test case 2
+    x,n = 6.0,5.0
+    expected_output = 6480.0
+    assert polynomial_derivative(x,n) == expected_output, "Test case 2 failed"
+
+    # Test case 3
+    x,n = 12.0,4.3
+    expected_output = 15659.0917
+    assert polynomial_derivative(x,n) == expected_output, "Test case 3 failed"
+
+    # Test case 4
+    x,n = 14.35,1.0
+    expected_output = 1.0
+    assert polynomial_derivative(x,n) == expected_output, "Test case 4 failed"
+
+if __name__ == "__main__":
+    test_polynomial_derivative()
+    print("All Polynomial Derivative tests passed.")