Final answer:
The derivative of the function y = 6x⁴ + 4 sin x is found by applying the power rule and the derivative of the sine function, resulting in y' = 24x³ + 4 cos x.
Step-by-step explanation:
To find the derivative of the function y = 6x⁴ + 4 sin x, we will use the power rule and the derivative of the sine function. Applying the power rule, the derivative of x⁴ is 4x³. The derivative of sin x is cos x. Hence, the derivative of 6x⁴ is 24x³ and the derivative of 4 sin x is 4 cos x. Summing these results, the derivative of the given function is y' = 24x³ + 4 cos x.
Note that if there are additional terms added together, this power rule of differentiation can be done multiple times and the solution is the sum of those terms. The following example illustrates the use of Equation 3.7.