Question

Find the following derivative:
(d/dx)((7 - x⁶)³/x⁶)

Answer 1

To find the derivative of the given expression (7 - x⁶)³/x⁶, use the quotient rule.

Step-by-step explanation:

In calculus, a derivative measures how a function changes as its input (independent variable) changes.

To find the derivative of the given expression (7 - x⁶)³/x⁶, we can use the quotient rule.

1. Differentiate the numerator using the chain rule: d/dx ((7 - x⁶)³) = 3(7 - x⁶)²(-6x⁵).
2. Differentiate the denominator: d/dx (x⁶) = 6x⁵.
3. Apply the quotient rule: (d/dx) ((7 - x⁶)³/x⁶) = (x⁶ * 3(7 - x⁶)²(-6x⁵) - (7 - x⁶)³ * 6x⁵) / (x⁶)².

Simplifying the expression further will give you the final answer.