Find dy/dx (dy)/(dt)=d/(dt)*(x^5+8)

Problem

d()/d(t)*(x5+8)

Solution

1. Identify the variables involved. We are asked to differentiate the expression x5+8 with respect to the variable t

2. Apply the sum rule for differentiation, which allows us to differentiate each term of the expression separately.

3. Apply the chain rule to the term x5 because x is assumed to be a function of t

4. Differentiate the constant term 8 with respect to t which results in 0

5. Combine the results to find the final derivative expression.

Final Answer

d()/d(t)*(x5+8)=5*x4d(x)/d(t)

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