Find the Derivative - d/dx (x^2)/5

Problem

d()/d(x)(x2)/5

Solution

1. Identify the constant factor in the expression. The expression (x2)/5 can be rewritten as 1/5⋅x2

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()/d(x)(x2)/5=1/5⋅d(x2)/d(x)

3. Apply the power rule to differentiate x2 The power rule states that d(xn)/d(x)=n*x(n−1)

d(x2)/d(x)=2*x

4. Multiply the constant factor by the result of the derivative.

1/5⋅2*x=(2*x)/5

Final Answer

d()/d(x)(x2)/5=(2*x)/5

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