Final answer:
The derivative of (4x³+9x+14)¹° is found by using the chain rule. It is 10(4x³+9x+14)⁹ times the derivative of the inner function, which is 12x²+9.
Step-by-step explanation:
Finding the Derivative of a Function
To find the derivative of the function (4x³+9x+14)¹°, we need to use the chain rule. The chain rule states that if you have a composite function, the derivative is the derivative of the outer function evaluated at the inner function, multiplied by the derivative of the inner function. In this case, we treat (4x³+9x+14) as the inner function, u, and u¹° as the outer function.
The derivative of u¹° with respect to u is 10u⁹, and the derivative of (4x³+9x+14) with respect to x is 12x²+9. Therefore, applying the chain rule, the derivative is:
10(4x³+9x+14)⁹(12x²+9)