Find the Derivative - d/dx 5x^5

Problem

(d(5)*x5)/d(x)

Solution

1. Identify the function as a power function multiplied by a constant coefficient, where the constant is 5 and the power is 5

2. Apply the constant multiple rule, which states that the derivative of a constant times a function is the constant times the derivative of the function.

(d(5)*x5)/d(x)=5⋅d(x5)/d(x)

3. Apply the power rule, which states that d(xn)/d(x)=n*x(n−1) Here, n=5

d(x5)/d(x)=5*x(5−1)

4. Simplify the expression by performing the multiplication and subtracting the exponents.

5⋅5*x4=25*x4

Final Answer

(d(5)*x5)/d(x)=25*x4

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