Find the Derivative - d/dx y=5x^(3p)

Problem

d()/d(x)*5*x(3*p)

Solution

1. Identify the function as a power function of the form y=a*xn where a=5 and the exponent n=3*p

2. Apply the power rule for differentiation, which states that d()/d(x)*a*xn=a⋅n⋅x(n−1)

3. Multiply the constant coefficient 5 by the exponent 3*p

5⋅3*p=15*p

4. Subtract 1 from the exponent to find the new power of x

3*p−1

5. Combine the results to write the final derivative.

Final Answer

d()/d(x)*5*x(3*p)=15*p*x(3*p−1)

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