Question

Find the derivative. y=3x⁴+6x³+1 Select one:

Answer 1

To find the derivative of the function y=3x⁴+6x³+1, use the power rule to differentiate each term. The derivative is y' = 12x³ + 18x².

Step-by-step explanation:

To find the derivative of the function y=3x⁴+6x³+1, we need to use the power rule of differentiation. The power rule states that if we have a function of the form f(x) = ax^n, its derivative f'(x) will be anx^(n-1).

Applying the power rule to each term of the given polynomial:

• The derivative of 3x⁴ is 12x³.
• The derivative of 6x³ is 18x².
• The derivative of a constant (like 1) is 0.

Therefore, the derivative of y with respect to x is:

y' = 12x³ + 18x²