Question

For the equation $y = 3x^5 + 4x^4 - 3x^3 + x^2 - 2x + 1$, the value of $\frac{d^5y}{dx^5}$ is _ _ _. (answer in integer)

Hint:

For fifth derivative of a polynomial, only terms with power $5$ or more surviveHere, $3x^5$ gives $3 \times 5! = 360$

Answer 1

Correct Answer: 360

Step 1: Which term survives.
Each derivative lowers the power by one, so after five steps only the $3x^5$ term is left.

Step 2: Use the shortcut.
\[ \frac{d^5}{dx^5}(3x^5) = 3 \times 5! = 3 \times 120 = 360 \]

Step 3: Answer.
\[ \boxed{360} \]