Answer :
Final answer:
To find the derivative g'(x) of the function [tex]g(x) = -3x^5(-7x^5)[/tex], the Product Rule is applied, resulting in [tex]105x^9 + 105x^9[/tex]
, which simplifies to [tex]210x^9[/tex]. The correct answer choice must be adjusted to reflect this simplification.
Explanation:
To compute the derivative of the function g(x) = -3x5(-7x5), we can use the Product Rule for differentiation. The Product Rule states that if u(x) and v(x) are functions of x, then the derivative of their product u(x)v(x) is u'(x)v(x) + u(x)v'(x). Applying this to g(x), let f(x) = -3x5 and g(x) = -7x5.
The derivatives of f(x) and g(x) are f'(x) = -15x4 and g'(x) = -35x4 respectively. Using the Product Rule:
g'(x) = f'(x)g(x) + f(x)g'(x) = (-15x4)(-7x5) + (-3x5)(-35x4)
Simplifying, we get:
g'(x) = 105x9 + 105x9 = 210x9
Therefore, the answer is c) -105x9 + 105x9, but we need to correct it while considering simplification to 210x9.
