Answer :
Final Answer:
The derivative of a power function ax^n with respect to x is given by nax^(n-1).
The derivative of the function h(x) = 6x^7 is h^(')(x) = 42x^6. Therefore, the correct option is (C) 42x^6.
Explanation:
The derivative of a power function ax^n with respect to x is given by nax^(n-1). Applying this rule to the function h(x) = 6x^7, we get h^(')(x) = 7 * 6x^(7-1) = 42x^6. This is because the power rule states that when you have x raised to a power n, the derivative is n times the coefficient, and the power reduces by 1.
In this specific case, the original function has a coefficient of 6, and the power is 7. Applying the power rule, the derivative becomes 7 * 6x^(7-1) = 42x^6. Therefore, the correct option is (C) 42x^6.
In summary, when finding the derivative of h(x) = 6x^7, we apply the power rule to get h^(')(x) = 42x^6. This result shows the rate at which the original function is changing with respect to x, and in this case, it's a constant multiple of 42 times x to the power of 6. The correct option representing this derivative is (C) 42x^6.
