Differentiate. -Find f'(x) for f(x) = (5x³ + 4)(3x⁷ - 5). A) f'(x) = 150x⁹ + 84x⁶ - 75x² B) f'(x) = 20x⁹ + 84x⁶ - 75x C) f'(x) = 150x⁹ + 84x⁶ - 75x D) f'(x) = 20x⁹ + 84x⁶ - 75x²

Question

Quizplus · Accepted Answer

The product rule is used to differentiate the given function. The product rule states that if f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + g(x)h'(x). In this case, g(x) = 5x^3 + 4 and h(x) = 3x^7 - 5. Therefore, g'(x) = 15x^2 and h'(x) = 21x^6. Substituting these values into the product rule, we get f'(x) = (15x^2)(3x^7 - 5) + (5x^3 + 4)(21x^6) = 45x^9 - 75x^2 + 105x^9 + 84x^6 = 150x^9 + 84x^6 - 75x^2.

Differentiate. -Find F'(x) for F(x) = (5x3 + 4)(3x7 - 5)

Differentiate. -Find F'(x) for F(x) = (5x³ + 4)(3x⁷ - 5)