Final answer:
The Python program uses the SymPy library to read a polynomial entered by the user and calculates its first derivative, which is then printed as the output.
Step-by-step explanation:
To address the student's need, we can create a Python program using the SymPy library to compute the derivative of a polynomial. Below is a simple program to illustrate this:from sympy import symbols, diffx = symbols('x')polynomial = input('Enter a polynomial in x: ')# Convert the input string into a SymPy expressioexpr = sympify(polynomial# Calculate the first derivative of the expressioderivative = diff(expr, xprint('
The first derivative is:',derivative)The first derivative of the polynomial entered by the user will be printed on the screen. Remember to install the SymPy library before running this script.To find the first derivative of a polynomial, we need to differentiate each term of the polynomial using the power rule. The power rule states that the derivative of x^n is n*x^(n-1), where n is the exponent of x. Differentiate each term of the polynomial separately, and combine the derivatives to get the first derivative of the polynomial. This will give you a new polynomial that represents the first derivative of the original polynomial.