Final answer:
To find the differential of the function y = theta^4 sin(8theta), apply the product rule and chain rule. First, find the derivative of theta^4 and sin(8theta) separately. Then, use the product rule to combine the two derivatives and get the differential of the function.
Step-by-step explanation:
To find the differential of the function y = theta^4 sin(8theta), we need to apply the product rule and chain rule. Let's start by finding the derivative of theta^4 and sin(8theta) separately.
The derivative of theta^4 is 4theta^3, and the derivative of sin(8theta) is 8cos(8theta).
Now, apply the product rule by multiplying the derivative of theta^4 with sin(8theta) and theta^4 with the derivative of sin(8theta). Finally, combine the two terms to get the differential of the function.
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