Question

Let \( f(x) = (x^3 + 2)^{30} \). If \( f^{(n)}(x) \) is a polynomial of degree \( 20 \), where \( f^{(n)}(x) \) denotes the \( n + h \)-order derivative of \( f(x) \), then the value of \( n \) is:

• A. 60
• B. 40
• C. 70
• D. 50

Hint:

For polynomials, the degree of the \( n \)-th derivative decreases by \( n \) for each differentiation.

Answer 1

The Correct Option is C

The degree of the derivative \( f^{(n)}(x) \) is calculated by differentiating the function \( (x^3 + 2)^{30} \).
Since the original function has a degree of 90, the degree of the derivative of order \( n \) will be \( 70 \). 
Hence \( n = 70 \).