Question

Differentiate g(x) = (x^[-5] + 3)(x^[-3] + 5).

A. g'(x) = -8x^[-7] - 25x^[-6] - 9x^[-4]
B. g'(x) = -8x^[-9] - 25x^[-4] - 9x^[-4]
C. g'(x) = -8x^[-9] - 25x^[-6] - 9x^[-4]

Answer 1

To differentiate the function g(x) = (x^(-5) + 3)(x^(-3) + 5), apply the product rule and the power rule, then simplify and combine the terms to find the final derivative.

Step-by-step explanation:

To differentiate the function g(x) = (x^(-5) + 3)(x^(-3) + 5):

1. Apply the product rule, which states that if f(x) = u(x)v(x), then f'(x) = u'(x)v(x) + u(x)v'(x).
2. Take the derivative of the first term, (x^(-5) + 3), using the power rule, which states that if f(x) = x^n, then f'(x) = nx^(n-1).
3. Take the derivative of the second term, (x^(-3) + 5), using the power rule.
4. Simplify the expressions and combine the terms to get the final derivative.

The correct answer is g'(x) = -8x^(-7) - 25x^(-6) - 9x^(-4), so option A is the correct choice.