sympy import symbols, diff

Define the variable and the function

x = symbols('x') f = -3 / (4 * x3) + 1 / (2 * x5)

Compute the derivative

f_prime = diff(f, x) f_primeThe derivative of the function

$f(x) = -\frac{3}{4x^3} + \frac{1}{2x^5}$

is

$f'(x) = \frac{9}{4x^4} - \frac{5}{2x^6}.$

Would you like a detailed explanation of the steps involved?

Here are 5 related questions for further exploration:

1. How do we handle derivatives of fractions with higher powers of $x$?
2. What is the second derivative of this function?
3. How can we simplify this derivative further?
4. How would the derivative change if an additional term was added?
5. What are the critical points of this derivative?

Tip: Always double-check your exponents when dealing with derivatives involving fractions to avoid errors.