Question

Find the derivative of the algebraic function f(x) = (c⁶- x⁶)/c⁶x⁶, where c is a constant.

Answer 1

To find the derivative of the function f(x) = (c⁶ - x⁶) / (c⁶x⁶), we can use the quotient rule. f'(x) = -6(c⁶ - x⁶) / (c⁶x⁶)^2

Step-by-step explanation:

To find the derivative of the function f(x) = (c⁶ - x⁶) / (c⁶x⁶), we can use the quotient rule.

The quotient rule states that if you have a function in the form g(x) / h(x), the derivative is given by (h(x) * g'(x) - g(x) * h'(x)) / (h(x))^2.

Applying the quotient rule to our function, we get:

f'(x) = ((c⁶x⁶)(-6x⁵) - (c⁶ - x⁶)(6c⁶x⁵)) / (c⁶x⁶)^2

Simplifying the expression, we get:

f'(x) = -6(c⁶ - x⁶) / (c⁶x⁶)^2